West Germany, which gave up a gift goal after only four minutes, drew even with six minutes remaining yesterday to tie Uruguay, 1-1, in a battle between two-time World Cup winners in Mexico City.

In a Group B game in Toluca, Paraguay defeated Iraq, 1-0, on a 35th-minute goal by Julio Cesar Romero.

In the third game of the day, a night match in Nezahualcoyotl, Preben Elkjaer scored in the 59th minute to give Denmark a 1-0 victory over Scotland.

West Germany, bidding to add to the titles it won in 1954 and 1974, got off to a bad start in the Group E match at Queretaro. Lothar Mattheaus, in attempting a back pass, put the ball at the feet of Antonio Alzamendi, who outmaneuvered goalkeeper Toni Schumacher to score off the crossbar.

The West Germans then toughened and generally dominated play the rest of the way, but it looked as if their efforts would go unrewarded until six minutes from the end when Klaus Allofs took a pass that split the Uruguayan defense and beat the advancing goalie with a left-footed shot.

Uruguay, which won the inaugural World Cup on home soil in 1930 and repeated in Brazil 20 years later, was booed by the crowd in the second half as it apparently decided to sit on its lead.

The West Germans, who emphasized defense early, were forced to change tactics after giving up the early goal and from that point on virtually lived in Uruguay's half of the field. That left them open to counterattack and they nearly paid the price in the 70th minute when Enzo Francescoli got around the last defender, but then shot into the side netting of an open goal.

Elkjaer, who played an outstanding game for Denmark, dribbled around Scotland's Willie Miller at the top of the penalty area and sent a 10-yard kick off the far post and into the net.

Earlier in the second half, striker Michael Laudrup's angled pass found Elkjaer clear in front of the Scottish net, but he was too deep and his shot hit the netting.

Scotland's best chance to tie came in the 72nd minute, when Gordon Strachan's crossing pass nearly sneaked in at the near post. Goalie Troels Rasmussen dropped on the ball just before it crossed the line.

Graeme Souness missed wide with a dead-on kick from 25 yards just a minute later.

Paraguay and Iraq, neither of which is expected to survive the first round, played with spirit and determination.

Romero scored the only goal of the game when he took a 40-meter pass from Adolfino Canete and lobbed the ball over goalie Raad Salan from about 10 meters as Salan came off his line.