The Bramall Lane side ended a miserable run of dour games without a win, while Gary Johnson's outfit are now in danger of being sucked into a relegation battle.
Henderson, who snatched hat-trick when the clubs last met at Ashton Gate in November, was handed two chances earlier in the game.
Kevin Geary engineered a chance for the big striker with a precise cross from the right which the unmarked Henderson duly headed high and wide of the target.
The lively Ward was the provider on 19 minutes, this time Henderson out-jumped his marker to steer the ball over the top from eight yards.
Arsenal teenager Kyle Bartley drilled in a right-foot strike which took a deflection off centre-back Liam Fontaine but Dean Gerken managed to block the shot.
Minutes later, the Bristol keeper conjured up another spectacular stop after palming away Mark Yeates' fierce drive from a tight angle.
Gerken foiled United again as the Sheffield side as grabbed a stranglehold on the game. Camara was the first to react as Bristol struggled to clear but his snapshot from 10 yards blocked by the keeper.
Bristol capitulated in the 49th minute when Bartley's probing ball down field found Camara.
The ex-Wigan striker coolly took the ball in his stride before lashing it into the top corner of the net with Gerken helpless.
Yeates saw his free-kick saved by Gerken and Ward drilled the ball over the top as United continued to overrun the fragile City rearguard without being able to kill off the game.
It was left to Henderson to relieve the pressure in the 61st minute when he stretching to meet a Ward cross and beat Louis Carey with a firm header at the near post.
City went close late in the game when Carey met Paul Hartley's corner but his looping header from six yards hit the top of the bar and bounced away to safety.