In a tight encounter in Dublin, Jonathan Walters put the hosts ahead in the 38th minute, although he appeared to be offside when he finished from close range.
Scotland levelled just two minutes into the second half as Shaun Maloney’s shot took a heavy deflection off John O’Shea and flew into the far corner.
The result keeps Scotland firmly in contention to qualify automatically for Euro 2016 from Group D while Ireland have work to do in their remaining four matches.
Poland’s 4-0 victory over Georgia means they remain top of the group, with Germany, Scotland and Ireland battling for qualification behind them.
With the onus on Ireland to take all three points at the Aviva, Martin O’Neill opted to start with Daryl Murphy up front, leaving Robbie Keane, whose two cousins died after a work accident earlier this week, on the bench.
Scotland, who started the day third in the group after winning the reverse fixture against Ireland 1-0 in November, handed starts to Matt Ritchie, Craig Forsyth and Celtic’s Charlie Mulgrew.
There was little to choose between the sides in the early stages, with chances at a premium at both ends.
Ireland right-back Seamus Coleman was seeing plenty of the ball in advanced positions, but he was unable to pick out a green shirt as keeper David Marshall and Forsyth cut out crosses in quick succession.
But the deadlock was broken in the 38th minute when Marshall had to tip Murphy’s looping header over and Ireland scored from the resulting corner.
Marshall made a good reaction save after Murphy got his head to Robbie Brady’s delivert, but Walters was on hand to stab home the rebound from point-blank range and Scottish appeals for offside went unanswered.
Murphy might have helped himself to a second on the stroke of half-time, but could not react quickly enough to get a meaningful touch to Brady’s corner as it bounced across the six-yard box.
Scotland levelled inside two minutes of the second half as Maloney, who scored in the winner in the reverse fixture, curled in a shot that was going wide until it deflected off O’Shea and past Shay Given.
Murphy could have quickly restored Ireland’s lead after being put through by Wes Hoolahan, but he was denied by Marshall who had little to do for rest of the game as Ireland struggled to regain the initiative.
A scrappy game produced an increasing amount of niggling fouls and unforced errors from both sides but Ireland, who replaced Whelan with James McClean in the 67th minute, remained largely in control with crosses into the box their most potent threat.
Keane received a massive roar from the home supporters when he replaced Hoolahan with 20 minutes remaining and almost immediately tested Marshall with a left-footed effort from the edge of the box.
Scotland had their backs to the wall in the closing stages but O’Neill’s side, aided by Shane Long who came on for Murphy, could not find the winner which would have made such a difference to their chances of reaching the 2016 finals in France.