Trinidad and Tobago held on for a courageous draw despite playing the whole of the second half with 10 men.
Soca Warriors defender Avery John picked up the first red card of the World Cup after two reckless tackles.
Cornell Glen had Trinidad and Tobago's best chance with a thumping drive that hit the bar, but they were pinned back for much of the game.
Marcus Allback and Zlatan Ibrahimovic both should have done better with good chances but the islanders held on.
Trinidad and Tobago were forced to make a change before the kick-off as goalkeeper Kelvin Jack suffered a last-minute injury on the way back to the dressing room after the warm-up session.
West Ham's Shaka Hislop was drafted in to replace him.
And he was almost called in to action inside five minutes when Henrik Larsson's fierce free-kick from the edge of the penalty area narrowly fizzed past the post.
The Swedes, who have yet to win since qualifying for the World Cup last October, controlled the first half and looked more assured in possession, making the Soca Warriors chase the game.
Trinidad and Tobago's most likely source of a goal in the first half looked to be from long-range as Sweden pinned the opposition in their own half.
And it was Carlos Edwards' drive from distance that was the best of the Trinidad and Tobago chances.
Substitute Glen almost gave Trinidad and Tobago a shock lead when Cornell Glen thumped a drive off the bar while at the other end Hislop superbly kept out an Ibrahimovic volley.
Sweden became increasingly frustrated and the Trinidad and Tobago players stood firm to repel the Swedes' constant attacks.
However Trinidad and Tobago have picked up an historic point on their World Cup debut.
