From a short corner, Maloney squeezed the ball into the feet of Scott Brown, whose back-heel allowed the winger to curl an exquisite shot home.
There was a late scare for the Scots as Grant Hanley’s header hit his own bar.
But the win draws Scotland level with the Irish and Germany on seven points after four games in Group D – with Poland three points clear of the trio.
Former Celtic manager Martin O’Neill had spoken of his belief that his Irish side could win on his return to Celtic Park. Instead, it was his successor at the club, Gordon Strachan, who enjoyed the happier homecoming.
Another of the pre-match talking points was the expected booing of the Scots-born Ireland winger Aiden McGeady and his reception was suitably hostile – he was treated by the home fans as the pantomime villain.
From the outset, the pace of the game was frenetic. The tackling was tenacious and, at times, downright careless, leading to early bookings for Hanley, McGeady and his Ireland team-mate, Jeff Hendrick.
The passion on show almost made up for the dearth of football, with precious few chances created in the opening half-hour.
Jon Walters and Darron Gibson did force David Marshall into saves, but there was little to worry either goalkeeper.
Scotland’s play under Strachan has come to be typified by slick attacking play and it was one such passage that almost brought about the opening goal.
Steven Naismith foraged away before picking out Maloney on the right. The winger’s cross was whipped in for the charging Charlie Mulgrew, but his header flew wide.
That was the cue for some concerted Scots pressure, which should have been rewarded only for Steven Fletcher to somehow fail to connect with another Maloney cross.
O’Neill’s side lifted their game at the start of the second period and Marshall saved a close-range Shane Long header before brilliantly turning away a McGeady volley.
Fletcher’s replacement, Chris Martin, almost made an instant impact, firing just wide after good play again by Maloney and Naismith.
However, just as the visitors had tried to shut up shop by taking off Long and adding a fifth midfielder, Scotland made the breakthrough.
It leaves Group D very open as the qualifiers come to an end for 2014.