The Irish dominated an occasionally tetchy game and deservedly took the lead in the 38th minute through forward Jon Walters, after Scots’ keeper David Marshall had saved a Darryl Murphy header.
However, Shaun Maloney, who scored in the 1-0 win for Scotland when the two sides met at Celtic Park in November, levelled with a shot which deflected off Irish skipper John O’Shea seconds after the restart.
Ireland shrugged off that blow and roared back but the visitors held out, unconvincingly at times, for the point to go above Germany into second place in Group D.
The world champions, however, should restore their advantage later in the evening against Gibraltar, while leaders Poland showed again their qualifying credentials with a 4-0 win over Georgia.
It was a better point for Scotland than Ireland who started without two of their most influential players in Robbie Keane and Aiden McGeady.
Skipper Keane, whose cousins Alan and Steve Harris died after a work accident earlier this week, was included among the substitutes, as was McGeady after sitting out training on Friday with a hamstring complaint, while striker Murphy and midfielder Jeff Hendrick got the nod to start.
Strachan sprang a surprise of his own when he named Derby full-back Craig Forsyth in his team for his first competitive game, after three caps in friendlies.
There was a place too for Celtic’s Charlie Mulgrew, just his fourth appearance for club and country after a five-month injury lay-off, as Steven Fletcher was asked to lead the line.
Scotland fans had been allocated around 3,5000 tickets but there were many more inside the stadium to watch the green and white jerseys ruffle up the visitors, with Forsyth looking especially vulnerable.
In the 17th minute Ireland’s Glenn Whelan powered a shot from 30 yards over Marshall’s crossbar to end another decent passage of play from O’Neill’s men, before being booked by Italian referee Nikola Rizzoli for a foul on Steven Fletcher.
On the half-hour mark Ireland’s Scottish-born midfielder James McCarthy picking up a yellow for leading with his elbow in an aerial challenge on Russell Martin, who required treatment before continuing.
Ireland’s goal came after Marshall tipped a header from Murphy over the bar for yet another Irish corner.
When Robbie Brady’s cross came in from the right Murphy’s close-range header was blocked by the Scotland keeper but only to Walters who had the easiest task in knocking it over the line, albeit from a suspiciously-looking offside position.
However, there was no doubt that the Irish had deserved their interval lead.
Ikechi Anya replaced Matt Ritchie for the start of the second-half and within seconds were level when Maloney linked with the Watford winger and from 25 yards out, curled a shot past Irish keeper Shay Given with the aid of a clear deflection off the luckless O’Shea, with the visiting support celebrating regardless.
The Irish, though, perhaps should have restored their lead moments later when Murphy found himself up against Marshall but the Scots keeper saved with his legs and Strachan’s side ultimately survived.
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 Wes 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.