Chris Makin fired the visitors ahead after 15 minutes from a pass by Gunnar Halle, but Tranmere levelled seven minutes later when Chris Malkin put a looping header over the goalkeeper, Paul Gerrard, from a free-kick. Dave Higgins then missed a fine chance to put them in front early in the second half.
Oldham enjoyed a good spell, but were thwarted by the home goalkeeper, Eric Nixon, who made some excellent stops. Tranmere went ahead in the 74th minute when Ian Muir headed home from Brannan's cross, and a minute from time, Brannan turned goalscorer with a superbly struck shot from 20 yards.
Paul Simpson's hat-trick maintained Derby's advance up the first division, and left Portsmouth perilously close to the relegation zone. The former Manchester City winger sealed Derby's 3-0 win with all his goals in the second half of a frantic and scrappy contest.
Derby had a goal disallowed in the third minute, despite Ray Daniel appearing to be well over the line when he cleared after Portsmouth's Darryl Powell looped a header over his own goalkeeper, Alan Knight.
There was no dispute about Derby's opening goal, two minutes into the second half, however. Jason Kavanagh's cross flicked off the head of Guy Butters, and Simpson connected with a left-foot volley that gave Knight no chance.
Simpson's second came on 76 minutes. Lee Russell upended him 25 yards out, and a bending free-kick left the Pompey goalkeeper grasping at thin air.
Portsmouth rallied briefly with Lloyd McGrath going close, but Simpson settled it a minute from time when he drove home from Marco Gabbiadini's pass.Reuse content