Scotland broke the deadlock with five minutes gone at Portman Road to end a barren three-game spell for the former Wigan and Swansea striker.
Leadbitter made sure of a deserved victory for Roy Keane's side with a second-half penalty that leaves the Tractor Boys just outside the play-off places.
Theo Robinson dragged a 25-yard shot wide with just seven seconds gone as Millwall threatened straight from the kick-off, but it proved a false dawn as the home side surged ahead after five minutes.
Tamas Priskin and Carlos Edwards exchanged passes down the right wing before the latter crossed for Scotland to fire home his fifth goal of the season.
The Lions initially reacted positively to going a goal down, James Henry and Steve Morison both trying their luck from outside the penalty area.
Damien Delaney steered a header wide from Leadbitter's outswinging corner six minutes before the half-time interval, while a Tommy Smith headed effort was blocked by Henry.
The visitors came close to equalising late on in the first half, but Paul Robinson's header from Nadjim Abdou's cross looped just over.
Danny Schofield blazed over two minutes after the restart before Ipswich launched a swift counter-attack following Henry's wayward corner and Jack Colback eventually shot wide from just inside the penalty area.
Priskin continued to pose Millwall plenty of problems and won his side a penalty when he was fouled by Danny Shittu after getting on the end of an Edwards throw-in. Leadbitter made no mistake with his 56th-minute spot-kick, blasting the ball beyond David Forde for his first goal in over two months.
Kenny Jackett immediately sent on Darren Carter and John Marquis in the hope of getting a foothold in the game and Scott Barron sent a 30-yard shot crashing over as the Lions looked to hit back straight away.
Scotland was unfortunate not to double his tally for the afternoon on the hour mark as his low shot from 20 yards was saved well by the feet of Forde, who moments later denied Leadbitter from a similar distance.
Shittu saw his weak 12-yard header comfortably dealt with by Marton Fulop before Keane introduced highly-rated youngster Connor Wickham with 25 minutes remaining.
Robinson also failed to hit the target with a header as Millwall continued to surge forward and the visitors were kept at bay by some brave defending after 85 minutes as Henry and Morison were both denied in the space of 60 seconds.
Leadbitter curled a 35-yard free-kick wide and Wickham had a well-struck right-footed shot blocked by Shittu late on.