Jimmy Connors was upset by Vijay Amritraj, 6-3, 6-2, tonight in the $200,000 WCT Invitational round-robin tournament, then injured his left wrist in a post-match altercation with a teen-age male tennis fan.

Bjorn Borg overpowered John Alexander, 6-3, 6-1, and Eddie Dibbs rallied to defeat Ilie Nastase, 2-6, 6-3, 6-4, in the first two matches of this second day of competition.

Connors played poorly in losing to the 28th-ranked Amritraj, then was leaving the court with his wife, Patti McGuire Connors, a former Playboy playmate, when the fan grabbed her and t ried to kiss her. Connors punched him, suffering a possible sprained wrist.

Police arrested the fan, but no charges were immediately filed.

If Connors withdraws from the tournament, 23-year-old John Sadri, ranked 20th in the world, is on call to replace him.

Borg moved to a 2-0 record in the six-player tournament, while dropping Alexander to 0-2. The other players are 1-1.

Borg, 23, was in command from the outset. The Swede, ranked first in the world, exhibition his usual array of impressive ground strokes and continually kept the powerfully built Alexander off balance with an assortment of passing shots.

Borg broke Alexander's serve in the fifth and ninth games of the first set.

With the score 2-2, Borg passed Alexander twice and forced an error at the net to gain the service break. A crisp down-the-line backhand and another forced error proved the Australian's undoing in the ninth game.

Borg was overwhelming in the second set. He held a 5-0 lead with service breaks in the second and fourth games before Alexander, a serve-and-volley player, held service in the sixth game.

Two Alexander double-faults contributed to Borg's first break, and several unforced errors contributed to the second.

It was disclosed that Alexander had been suffering back spasms, but the 28-year-old was unavailable for comment following his match with Borg.

There was no indication that Alexander would withdraw from the six-day tournament that ends Sunday by matching the players with the two best records. t

Pugnacious Eddie Dibbs rallied from a first-set deficit to hand Ilie Nastase of Romania a 2-6, 6-3, 6-4 defeat in the second match of the night.

Nastase dominated the first set, but Dibbs came alive with tenacity to overwhelm the Romanian. Dibbs and Nastase are 1-1 in the tournament.