Long-range specialist Darren Edmondson kept York's play-off bid on course with a 40-yard spectacular.
A game of more passion than skill saw his right-foot volley just before half time separate the sides.
It was a stunning shot which left Rovers keeper Scott Howie motionless on his line.
Playing in front of the back four it was Edmondson's third goal of the season. The other two have also been hit from way out but with his left.
His latest goal came at a time York were very much in need of a lift for 12 minutes earlier they had missed a penalty.
Referee Phil Joslin was right on the spot to see Rovers defender Kevin Austin bundle over Anthony Shandran but his decision angered a crowd of 8,248 - except for York's small travelling army of 135.
The penalty by Jon Parkin had keeper Howie going the wrong way but smacked the bottom of his right-hand post.
All the early pressure had come from Rovers, winners at Leyton Orient on Saturday, and badly needing a second home win of the year to ease the fears over their league status.
But the Inland Revenue, who are threatening to close the club next week, are a bigger threat to York than was Rovers' weak attack.
The best chances fell to lanky striker Paul Tait. From the first he was left looking hopefully for a penalty after being pushed off the ball by Chris Brass but then later chose to pass to his partner Giuliano Grazioli when he should have shot.
Rovers had to wait a long time, into the 65th minute. before defender Sonny Parker got in a long shot which was well covered by Michael Ingham.
Right on time Rovers thought they had saved the game from a retaken corner when Grazioli headed in at the far post. But the flag was up for offside.