Trinidad and Tobago held on for a courageous draw despite playing the whole of the second half with 10 men.
Henrik Larsson's shot is blocked by Dwight Yorke
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.
The result means that England will progress to the next round if they beat Trinidad and Tobago on Thursday.
While Sweden will be looking to take three points from Paraguay on the same day.
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.
Shaka Hislop is congratulated by his Trinidad and Tobago team-mates
But Sweden looked the more likely to find the net and Larsson had a header drift inches over after a Freddie Ljungberg cross and Christian Wilhelmsson drove a stinging shot straight at Hislop.
Anders Svensson and Ibrahimovic both had half-chances to make the breakthrough, but the half-time whistle was met with cheers by the Trinidad and Tobago supporters who were relieved not to have conceded.
Their cheers turned to jeers soon after the break as John picked up the his red card when he clattered into Wilhelmsson.
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.
Marcus Allback should have given Sweden the lead 10 minuted before time but Hislop again pulled off a fine save to keep the score level.
But the Caribbean side picked up an historic point on their World Cup debut.
Trinidad and Tobago: Hislop, Avery John, Sancho, Lawrence, Gray, Birchall, Edwards, Theobald (Whitley 66), Samuel (Glen 53), Stern John, Yorke.
Subs Not Used: Andrews, Charles, Cox, Jack, Ince, Jones, Latapy, Scotland, Wise, Wolfe.
Sent Off: Avery John (46).
Booked: Avery John, Yorke.
Sweden: Shaaban, Linderoth (Kallstrom 79), Mellberg, Lucic, Edman, Ljungberg, Alexandersson, Anders Svensson (Allback 62), Wilhelmsson (Jonson 78), Ibrahimovic, Larsson.
Subs Not Used: Alvbage, Andersson, Elmander, Hansson, Isaksson, Nilsson, Rosenberg, Stenman, Karl Svensson.
Ref: Shamsul Maidin (Singapore).
Fifa man of the match: Dwight Yorke.
Sweden have failed to win their opening match at a World Cup for the seventh consecutive time. Their last win in an opener dates back to 1958 when they beat Mexico 3-0. Sweden are yet to win in 2006. They have drawn five times and lost once this year. This was their third goalless draw of the year.
Trinidad & Tobago's Avery John became the first player at the 2006 World Cup to be sent off. He follows in the footsteps of Croatia's Boris Zivkovic who received the first red card in 2002.
At the age of 37 years and 108 days, Shaka Hislop became the oldest player at the 2006 tournament. He ranks 20th on the all-time list which is led by Roger Milla (Cameroon) who played at the age of 42 years and 39 days in 1994.