They have lost just one of their last ten games, and manager Gary Johnson is determined to finish the season in style.
For Hartlepool, though, their League One place hangs by a thread after one of their poorest displays of the season.
City were much the better side in the first half, and were full value for their two-goal lead at the break.
Hartlepool's relegation nerves were showing both in defence and attack as City scored from two of their three chances.
First, on 13 minutes, they cashed in on a slip by home defender Michael Nelson wide on the right and, before the home defence could recover, David Noble scored from a tight angle on the left of the area.
City keeper Adriano Basso saved a Lee Bullock header on his own goal-line, and then did well to keep out an angled shot from Eifion Williams.
But it was City that carried more threat and home keeper Dimi Konstantopoulos pulled off a double save in a crowded six-yard box after a shot from the right by Scott Brown.
City's second goal arrived on 38 minutes when Marc McCammon got away on the right and crossed low to the far post, where Alex Russell was unmarked as he lashed in a ten-yard shot.
There was a short spell soon after the break when Hartlepool threatened to get their game together, Richie Humphreys shooting wide as he stretched for the ball, and Basso saving well from Hugh Robertson's 25-yard free-kick and from a close-range effort by Humphreys.
City coped with the home team's attempts to fight back after the break, until seven minutes from the end when Williams headed in from close range after a left-wing cross from sub Matty Robson.
But it was too late to save the game for the home team.