A dull first half exploded into life after the break as both countries added some cutting edge to their graft.
Ireland seized the initiative in the 48th minute thanks to a smart finish from winger Wes Hoolahan, who was dangerous throughout and deserved his goal after good work on the opposite flank by team-mate Seamus Coleman.
That seemed to shake the Swedes from their slumber and they began attacking more, led by captain Zlatan Ibrahimovic who was seeking to become the first player to score at four Euros.
Whereas the opening 45 minutes featured few chances and a couple of shots, the second half was completely different as both sides took risk and committed more men to attack.
Sweden have never lost a competitive fixture to Ireland and preserved that record after Ibrahimovic's cross in the 71st minute caused confusion in the penalty area and defender Ciaran Clark's attempted diving header-clearance flew past his goalkeeper for the equaliser.
The frenetic pace was maintained as both teams tried unsuccessfully to find the winning goal but Martin O'Neill and Erik Hamren will have to be satisfied with a point.
- Ireland get the match's first effort on target as Jeff Hendrick collects a knock-down from Jon Walters in the ninth minute and drives a shot at Andreas Isaksson but the big Swede palms it away.
- Big miss by skipper John O'Shea in the 17th minute. Six yards out from goal, he miscues his effort and cannot get a clean connection to give Ireland the lead.
- Hendrick does his best to break the deadlock. He curls a shot from distance that canons back off the crossbar but still goalless after 31 minutes.
- Sweden get their first corner in the 38th minute. The ball eventually finds Ibrahimovic but under pressure from Wes Hoolahan, the Swedish skipper skies his shot.
- It only takes Ireland three minutes to make the breakthrough. A mazy run from Coleman down the right and his clipped pass finds Wes Hoolahan who cracks in a half-volley past Isaksson.
- Sweden almost find an equaliser immediately as O'Shea's sliced clearance draws a smart save from his goalkeeper Darren Randolph. The rebound falls to Emil Forsberg who smashes his shot wide with the whole goal to aim at.
- After sustained pressure, Sweden get their equaliser in the 71st minute through an unlikely source. Ibrahimovic's cross from the left is diverted into his own net by the unlucky Ciaran Clark.
- The team in green almost respond immediately as Hendrick is free on the right but his shot is well saved by Isaksson.
The talking point
Deep-lying defences have so far proved effective against several of the competition's top strikers. England's Harry Kane, Poland's Robert Lewandowski and Spain's Alvaro Morata have been shackled effectively. Ibrahimovic also found it difficult to find any space and was largely isolated. The top scorers at the last edition managed just three goals. A similarly low haul could be in store in France.
Man of the Match
Nicknamed the Irish Messi (or Wessi), Hoolahan was a delight to watch. Deployed on the right side of the Ireland's attack, the winger tormented the Swedish defence with his pace, dribbling and sheer determination. A piece of skill in the second half, he switches the ball from one foot to the other and fools the opposing defender, summing up his confidence. He showed wonderful technique with his goal.
What the result means
Ireland ended their unwanted run of defeats in the Euros that stretched back to 1988 with this draw. The manner of the equaliser will be heartbreaking but there were plenty of positives for O'Neill to work with. The Irish will be underdogs in their next two games against Belgium and Italy but they should have nothing to fear after this committed display. For the Swedes, they were lucky to come away with a point and will need to find a way to supply Ibrahimovic with more support up front.
Sweden had seven shots in total but not a single one were on target, their equaliser coming from an own goal. Ibrahimovic and company will need to find their shooting boots for the next game against Italy.
What they said
Hoolahan: "It was a fantastic set up by Seamus Coleman, I caught it on the half-volley and was delighted. To get a goal for Ireland in the Euro is a great achievement. The boys were unlucky but we'll take the point. We created a lot of chances. In the first half we were excellent and at the start of the second half as well. The boys should be proud of themselves.
"It's a great point in the end. We will look forward to playing Belgium next, watch tonight and see how it goes."