Bjorn Borg and John McEnroe, the contenders for the No. 1 world ranking in tennis for 1979 that will be ultimately decided here this week, won their opening matches tonight in the $400,000 Colgate Grand Prix Masters Tournament at Madison Square Garden.

Borg -- winner of 80 of 86 singles matches and 12 tournaments, including his fourth French Open and Wimbledon titles last year -- served mightily and exerted constant pressure with blistering service returns and passing shots in avenging his U.S. Open loss to Roscoe Tanner, 6-3, 6-3.

McEnroe, victor in 89 of 100 singles matches and 10 tournaments in 1979, including the World Championship Tennis playoffs and the U.S. Open, was inconsistent off the ground, but assured enough in his serving and volleying to beat Harold Solomon, 6-3, 7-5.

Looming as formidable obstacles to an eventual battle of the titans in this final playoff for the top eight singles players in the worldwide 1979 Colgate Grand Prix, however, are Jimmy Connors and Guillermo Vilas, both of whom have been working hard to regain their former world-beating form and make 1980 a year of more major titles and fewer disappointments than 1979.

Connors, trimmed to fighting weight of 152 pounds and insistent that he has reconciled his family life with the demands of top-level tennis, wasted a 4-0 lead in the first set with a patch of sloppy play and then rolled over Spaniard Jose Higueras this afternoon, 6-3, 6-0. Connors lost only six points in the second set.

Vilas -- serving and volleying on the medium-fast, swimming-pool-blue synthetic carpet as if he were still playing on the fast grass on which he won the Australian Open title last week -- beat Vitas Gerulaitis impressively, 6-4, 6-7, 6-3.

Thursday's pairings in the round-robin portion of the tournament -- the men's equivalent of the women's Colgate Series Championship played last week in Washington -- have Gerulaitis against Solomon, and McEnroe against Vilas in the afternoon; Tanner against Higueras, and Borg against Connors at night. The two players from each four-man round-robin group with the best records will advance to Saturday's semifinals.

Borg was coming off a three-week layoff, but looked sharp and menaced in routine Tanner, who took him to 6-4 in the fifth set of the Wimbledon final last summer and beat him in the quarterfinals of the U.S. Open in near-by Flushing Meadow.

The glacial Swede shaved clean of the scraggly whiskers he usually sports "for good luck" at major tournament came out hitting hard and accurately and broke Tanner's serve at 15 in the first game of the match.

In the second game he demonstrated that he was serving and volleying as well as he was returning and cracking his topspin passing shots so it became obvious rather quickly that Tanner was destined for a short match and a long night.

"I felt a lot of pressure playing Roscoe in my first match but I felt good," Borg said. "It was very important that I broke him in the first game and then I found that I was serving well also, so I was very, very confident after the first two games."

When Borg is confident he is almost impossible to beat, and tonight he was hitting with pace an depth that gave Tanner no openings. Only twice did the left-handed Tennessean get to deuce on Borg's serve, and he never had a break point.

Tanner has given up the frizzy permanent that he adopted last year and has gone back to his old straight haired look but Borg's power was enough to curl his coiffure.

"I didn't put a much pressure on him as I could have," Tanner said. "I didn't get enough first serves in and missed a few volleys."

Tanner put only 49 percent of his first serves in court and overhit too many first volleys, trying for the kill too quickly against an opponent who was returning superbly.

"Borg served a lot better than he did at the Open, especially his second serve. It was harder. He was hitting it deeper, and moving it around. It was difficult to attack.

McEnroe, who received a check for $360,000 before the tournament began for topping the season-long Grand Prix point standings in both singles and doubles, was not nearly as sharp overall, but at the net he was "Mac the Knife."

Solomon challenged him all the way with forceful returns and passing shots, especially off the backhand, and cleverly moved over several steps when receiving to take away McEnroe's favorite serve, a wide slice to a right-hander's backhand.

"I figured if I could force him to serve down the middle he would be relying on his second-best serve," Solomon said. "I played him pretty well on his serve, but I couldn't do enough on my own serve."

McEnroe hit some ragged patches, and served five double faults at inopportune times, but hauled himself out of trouble with 11 aces and some sublime volleying when he needed it most.

The afternoon matches were played in a decidedly untennislike atmosphere thanks to busloads of children who were admitted free of charge and provided a constant undercurrent of squeals and screams.

Connors, who has not lost a set in five matches against Higueras, made numerous errors in the first set but got grooved in the second. Higueras twisted his chronically tender right ankle at the end of the first set, but said it was Connor's shotmaking that pained him more.

Higueras -- who has an ample black beard that becomes increasingly unkempt as he sweats, and a shirttail that hangs out and serves as a surrogate towel -- looked a bit like a bedraggled survivor of a shipwreck by midmatch. Connors left him marooned with no hope of rescue.

Connors was optimistic about his prospects for 1980. In a professionally disappointing 1979, he did not get past the semifinals of any major tournament and lost all six of his meetings with arch-rival Borg.

"I feel good. My game now is probably better than it has been in a year and a half, mainly because I've been working harder on my overall game and concentrating on getting in better shape," said Connors, who blames his subpar performance last season at least partly on the anxieties of becoming a husband and father.

"I think my outlook toward the game is a lot better. I play my tennis, I work hard on it, but once the tennis is over, it's over, Then I go home and spend time with my family," continued Connors, whose wife, Patti McGuire, former playmate of the year for Playboy magazine, and 5-month-old son Brett David are with him here, along with his mother and coach, Gloria.

"Then once my match comes along again, my family's over and I go out and play tennis. It took me awhile to be able to separate the two, particularly because it was a thrill to have a little one and to be able to spend time with him. It was a difficult adjustment, but once the adjustment was made it's improved not only my whole life."

While Connors was working in Los Angeles on his "overall game" the past month, Vilas was sweating in the scorching sun of the Australian summer, working on his net-rushing game, and his vastly-improved serve.He appears even more fit and muscular than usual.

He says the only motive was to win the once important Australian title, which he did for the second straight year over a weak field. But the fruits of his labor were evident as he served and volleyed confidently to thwart U.S. Open runner-up Gerulaitis in a splendid 2 hour 28 minute match.