Ciaran Clark was the culprit -- but he was placed in an invidious position as he tried to clear Zlatan Ibrahimovic's cross, only succeeding in heading the ball past Darren Randolph.
Prior to Sweden's equalizer, the Irish had looked the better team and had deservedly gone ahead early in the second half thanks to Wes Hoolahan's superb finish.
The draw meant Irish fans departed the Stade de France in northern Paris wondering what might have been, just as they had done seven years ago, the last time they had played at this venue.
On Ireland's return to the Stade de France, one of their key tasks was to contain Ibrahimovic. who had arguably dominated all the talk ahead of this Group E match, a section which includes Belgium and Italy.
Still yet to confirm his next club after leaving Paris Saint-Germain at the end of last season -- though it is widely reported he will sign for Manchester United
-- Ibrahimovic was also attempting to become the first player to score at four different European Championships.
Such is the internal Swedish focus on Ibrahimovic that there has even been a debate going on as to who is the squad's second-best player.
And for the Irish, there was the question to answer of just how to do you stop a man who has proclaimed himself a "King" and a "Legend."
Except, Ibrahimovic's first-half performance wasn't all that regal and certainly not what we've come to expect from a player who scored 38 goals for French champion PSG last season.
In the first half there was the occasional glimpse of the uber-confident Ibrahimovic, notably when he pirouetted away from a couple of Irish players, but it was a sign of his growing impotence that as the opening period wore on the Sweden captain dropped deeper and deeper.
"I think the players played Ibrahimovic exceptionally well," Ireland manager Martin O'Neill said after the game. "We forced him away from goal and it worked a treat."
Indeed the Republic of Ireland had the better chances in those first-half exchanges, notably when Jeff Hendrick swapped passes with Shane Long and rattled the bar with a curling shot.
Earlier another Hendrick shot forced Sweden goalkeeper Andreas Isaksson to push the ball away for a corner.
The Irish also came close to taking the lead on a couple of other occasions.
Defender John O'Shea was desperately close to connecting with Clark's header after a corner, while Long suffered similar frustration in trying to reach a Robbie Brady cross.
Prior to that chance, Brady had gone close with a shot that went just over the bar.
Within two minutes of the restart, Ireland went ahead with a well-worked goal that sent their hordes of traveling fans into ecstatic celebrations.
Seamus Coleman got the better of Emil Forsberg on the Irish right, and the Everton defender's cross was swept home by Hoolahan -- a superb strike.
The goal was a wake-up call for a somnolent Sweden.
Clark nervously hacked clear to concede a corner, and from that resulting set-piece pandemonium ensued in the Irish penalty box, but panic also gripped Forsberg, who badly sliced a great chance wide.
Ibrahimovic also began to stir and he almost snatched the equalizer with a deft low volley after Martin Olsson crossed.
And then, with 19 minutes remaining, Ibrahimovic finally got the better of the Irish with devastating results.
The 34-year-old scuttled clear of O'Shea, and his cross was inadvertently headed into the net by the unfortunate Clark.
Ibrahimovic was now really in the mood and as the game entered the final minutes, he almost got a touch another Olsson cross.
"We played brilliantly, but you have to put the ball in the net and we had the chances to do so," O'Neill said. "There is disappointment in dressing room, but the players shouldn't be down."
Disappointment was a word referenced more than once by Sweden coach Erik Hamren.
"We're not happy with the first 50 minutes. We have to do 300% now in the next game," he said, referring to Friday's match against Italy.
"To be a forward, you need support and for the first 50 minutes our forwards didn't have much to work with. Ibra was almost involved with the goal that we scored."
In Group E's second match of the day, an astute Italy performance saw the 2012 finalists overcome Belgium's team full of stars 2-0.
A first-half goal from Emanuele Giaccherini, orchestrated beautifully by Leonardo Bonucci's exquisite pass, and Graziano Pelle's thumping, stoppage-time volley were enough to send Antonio Conte's side top of the group.
If Italy's display exemplified the importance of tactics, teamwork and togetherness, then Belgium's was the polar opposite.
You could be forgiven for confusing the Red Devils' starting lineup for a Premier League manager's transfer wish list, but they regularly resembled 11 individuals rather than one cohesive unit.
Everton's Romelu Lukaku, widely rumored to be leaving the club this transfer window, had the pick of Belgium's chances but skewed his effort wide of the post when one-on-one with Italy goalkeeper Gigi Buffon.
The group's second set of fixtures take place on July 17 and 18, with Ibrahimovic's Sweden taking on Italy and Belgium facing Ireland.