The game looked set to end in a stalemate until Maloney produced a piece of magic 16 minutes from time to break the deadlock and earn Scotland the victory.
The win moves Scotland level on points with the Republic in Group D and ended Martin O’Neill side’s unbeaten start to qualifying.
As expected it was a fast and frenetic start to the contest and Jon Walters had the first chance of the game when he worked a one-two with Shane Long on the edge of the box and fired in a shot which was comfortably saved by David Marshall.
Scotland created their first opening on four minutes when Steven Fletcher rose above his marker John O’Shea to meet Shaun Maloney’s corner, but could only head his effort over the crossbar.
Grant Hanley had a lucky escape on 12 minutes when his poor touch was pounced on by Long and the Scotland defender lunged in on the Republic striker to stop him going clear on goal, but referee Milorad Mazic only gave a yellow card to the Scotland defender.
Aiden McGeady, who was getting jeered by the Scotland fans every time he touched the ball was the next player to be booked after a late tackle on Fletcher.
Scotland went close to breaking the deadlock on 34 minutes when Maloney fired over a cross to Mulgrew inside the box, but under pressure from Seamus Coleman the Scotland international was unable to direct his header on target.
Fletcher wasted Scotland’s best chance of the opening 45 minutes just before the break when Maloney picked him out inside the box, but the striker missed the ball trying to flick it with his left-foot when it would have been easier to hit it with his right foot.
Ireland had a half chance soon after the break when Walters flicked a ball onto Long inside the box from a corner, but the Southampton striker was unable to get enough power on his header to trouble Marshall.
Marshall came to Scotland’s rescue just before the hour mark when he got down well to push away McGeady’s left-footed volley from inside the box.
Scotland substitute Chris Martin really should have scored on 66 minutes when Naismith got down the right and picked out the Derby man inside the six-yard box, but the striker fired his shot wide of the target with the goal at his mercy.
Ireland almost gifted Scotland the opener on 74 minutes when Walters headed Mulgrew’s brilliant free-kick against his own crossbar for a corner.
The escape proved short-lived as Scotland made the crucial breakthrough from the resulting corner with a goal right off the training field.
Maloney worked a short corner to Brown and he laid the ball off to the Wigan man who curled his shot superbly into the far corner past Forde to spark jubilant scenes inside Celtic Park.
Ireland threw on Robbie Keane in the closing stages in search of an equaliser and they almost got in injury-time when Hanley flicked Robbie Brady’s free-kick onto his own crosbar, but Scotland held on to take all three points.