Giovanni Trapattoni's position has been under scrutiny since last summer's poor showing at Euro 2012 but the Irish have still not lost a qualifier away from home under his stewardship.
Sweden had the better chances with David Forde, making his first competitive start, twice saving well in the first half and again in the dying moments to preserve the stalemate.
Ireland dealt well with the threat of Sweden's star striker Zlatan Ibrahimovic and, although Austria overtook them with a convincing win over the Faroe Islands, they will be confident ahead of next Tuesday's game against them in Dublin.
Temperatures in the Swedish capital had plummeted to minus seven degrees by kick-off but it did not matter as the retractable roof was closed. The pitch, covered by an ice rink last weekend, also held up well despite initial fears.
Captain Robbie Keane, playing behind strike partner Shane Long, got into a good position early on but Jon Walters was unable direct a header goalwards. James McClean then appeared on the right and troubled Sweden goalkeeper Andreas Isaksson with a deep cross.
Sweden won a couple of corners in quick succession and got behind the Irish defence for the first time when Kim Kallstrom crossed for Sebastian Larsson, but the Sunderland man volleyed harmlessly across goal.
The Swedes gave warning of their quality, however, when dangerman Ibrahimovic headed on and Tobias Hysen connected with a well-directed volley. Forde showed no sign of nerves with a superb one-handed save to his right.
Ireland maintained their composure after the restart and it was just after the hour before Sweden seriously threatened again when Behrang Safari ran at the heart of the defence.
Ciaran Clark attempted to cut out his pass but succeeded only in finding Safari again and the Swede's square ball teed up a good chance for Larsson, but again the Sunderland player was wayward, this time slicing wide.
A goalless draw began to look like a good result for the Irish but they were not home yet with Ibrahimovic again threatening but fluffing a header and Alexander Kacaniklic miscuing a follow-up attempt.
Rasmus Elm almost snatched victory in the last minute but Forde produced another fine save to keep out his deflected shot.
|Sweden||Team Statistics||Republic of Ireland|
|0||1st Half Goals||0|
|3||Shots on Target||0|
|3||Shots off Target||4|
|61.3||1st Half Poss.||38.7|
|58.3||2nd Half Poss.||41.7|