Substitute Cole Stockton secured all three points for the hosts with a goal on the hour mark to separate the sides.
The victory lifts Tranmere above United after they slumped to a 3-2 home defeat to Hartlepool at Bramall Lane.
A brace from striker Steve Howard helped Hartlepool to all three points as United faltered, to end up level on points with Doncaster Rovers, who beat Preston 3-0 away from home.
Doncaster scored through Dave Syers, David Cotterill, Billy Paynter at Deepdale as the club continue to push towards the top two.
Brentford were held to a goalless draw at Shrewsbury, while Bournemouth beat Crawley Town 3-0 at Dean Court with goals from Brett Pitman, Eunan O’Kane and a Gary Alexander own goal.
MK Dons dropped out of the play-off spots after a 3-2 home defeat to Coventry, while Yeovil beat Portsmouth 2-1 at Fratton Park.
Crewe overcame Oldham 2-1 at Boundary Park, while Leyton Orient beat Walsall by the same scoreline at the Matchroom Stadium, and Carlisle beat Bury 2-1 at Brunton Park.