It was Chesterfield's fifth straight defeat and but for Roche it would have been an embarrassing afternoon for the home side.
The former Nottingham Forest keeper was beaten in the 76th and 90th minute as Tranmere at last found a winning formula on their travels.
Defeat was hard on Roche who kept his team in the match with a string of saves and left Tranmere cursing their luck and poor finishing.
The normally sharp Iain Hume was guilty of three glaring misses while Chris Greenacre also failed to find the net with only Roche to beat.
Chesterfield's defence was opened up too easily by Tranmere, whose only nervous moment came when John Achterberg made a superb save to deny Derek Niven.
That was Chesterfield's best chance but for all their effort they were second best in most areas.
Tranmere had set off with confidence and Hume should have scored in the fifth minute but he drove his shot straight at Roche.
Greenacre was twice in on goal but failed to make the chances count and there was a feeling that those misses could come back to haunt Brian Little's team.
Roche again made a superb save to keep out a Hume free-kick and when Niven got his head to a Kevan Hurst cross, Achterberg had to do just as well, flinging himself to his left.
Hume then hit the post twice but the goal finally came in the 76th minute when Michael Jackson jumped highest to head in Gareth Roberts' corner.
Wales full-back Roberts sealed the points for his team with an unstoppable 35-yard free-kick that flew into the top left corner but he was then booked by referee Mike Pike for celebrating with the Tranmere fans.