Both sides had play-off aspirations but turned in poor performances and there was little to excite the crowd of 2,300.
City's top scorer Andy Bishop could have added to his impressive total inside the opening two minutes with the best move of the game.
The Stevenage defence was carved wide open before Joe O'Neill passed to Bishop, but the striker's low angled shot ran beyond the far post when he should have hit the target.
The visitors hit back through Jon Nurse whose dangerous cross-shot flashed narrowly wide.
Stevenage took the lead on 21 minutes when Emanuel Panther lost the ball in midfield and his covering defenders failed to clear their lines before Dannie Bulman's cross was headed home by Louis.
Once ahead Stevenage seemed content to defend their lead and the Minstermen rarely threatened thereafter.
O'Neill flashed an effort wide from 18 yards and straight from the re-start Lee Andrews' cross flew off Bishop's thigh into the keeper's arms.
In swirling, windy conditions and on a heavy pitch against stern opposition, City failed to bring the game to life in the second period.
Boro had a chance to increase the lead when Chris Porter's clearance was charged down by George Boyd and Bulman followed up but his fierce effort flashed wide of the target.
Despite the generous additional time of five minutes, City still failed to test the visitors and their recent encouraging run came to a sorry end.