An early MK Dons goal was enough for the home side as Rovers lost 1-0 at StadiumMK.
It was a game of few real chances on goal, but a fine finish from Jason Puncheon in the sixth minute earned the Dons all three points.
Les Parry named an unchanged side following the goalless draw against Oldham, with the only change to the squad seeing new loan signing Chris McCready replacing Josh Macauley on the bench. Gareth Edds lined up against his former club in the centre of midfield.
After missing an early chance through Stephen Gleeson, the home side took the lead on seven minutes when Andros Townsend sent in a cross from the right wing, which was expertly converted by Jason Puncheon from just inside the area.
Rovers responded by winning a string of set pieces around the MK Dons area, but they were unable to turn them into goalscoring chances as the home defence stayed strong.
Townsend shot wide from outside the area for the home side on 23 minutes, and three minutes later Tranmere created their first attempt on goal as John Welsh fired narrowly wide of Willy Gueret's net from around 30 yards.
Craig Curran challenged Gueret for a loose ball on 28 minutes but the pair were beaten to the ball as a Dons defender cleared.
Another Welsh effort deflected wide for a corner on 37 minutes, with Zoumana Bakayogo firing over from the set piece that followed.
The home fans appealed for a penalty on 41 minutes when Jermaine Easter went down when challenging Ian Goodison and Ash Taylor for the ball but match referee Mark Haywood awarded a goal kick to the visitors.
Bakayogo brought a save out of Gueret in first half injury time, the closest Rovers came to finding the net in the opening 45 minutes.
Ian Thomas-Moore blocked a goalbound Dean Lewington header on 59 minutes, shortly before the Dons made their second change of the game as Jermaine Easter was replaced by Sam Baldock.
Ash Taylor headed over from a Paul McLaren corner on 61 minutes, with Chris Shuker replacing Gareth Edds moments later as Rovers switched to 4-4-2.
Welsh and Goodison were both booked in quick succession for fouls on Gleeson and Baldock respectively, with Logan following them into the referee's notebook ten minutes later.
On 81 minutes Shuker brought a save out of Gueret, the last chance of the game as Rovers went home empty handed.
MK Dons: Gueret, Lewington, Doumbe, McCracken, Gleeson, Easter (Baldock 59), Wilbraham, Woodards (Stirling 40), Puncheon, Leven, Townsend. Substitutes not used: Gobern, Powell, Morgan, Chadwick, Randall.
Tranmere: Daniels, Logan, Taylor, Goodison, Bakayogo, Welsh, McLaren, Edds (Shuker 61), Curran, Gornell, Thomas-Moore. Substitutes not used: Collister, Cresswell, Broomes, McCready, Mahon, Barnett.
Referee: Mark Haywood
Yellow cards: Welsh (65), Goodison (66), Logan (76), Gleeson (86)