Hunt, making his first appearance since October 23, came on at half-time and scored ten minutes from time to earn Brentford maximum points, after the home side wasted a host of chances to win the game.
Grant Smith had put Swindon into an unlikely lead on 21 minutes when he beat Michael Dobson - clashing heads in the process - to head in from the centre of the penalty area as Stuart Nelson strayed off his line.
But the home side were back on level terms a minute before the break thanks to Deon Burton, who made up for missing a sitter early on.
Hunt showed no ring rust after his spell on the sidelines with a groin injury latched onto Burton's cross to hand the points to Brentford.
Burton had earlier wasted a golden chance to score when he scuffed a tame shot wide of an open goal having beaten Swindon keeper Rhys Evans.
Chris Hargreaves should have scored from close range when he got on the end of Jay Tabb's corner but Jerel Ifil did well to clear off the line.
Ifil then kept out Eddie Hutchison's close range shot on 24 minutes amid calls for handball, but referee Phil Crossley indicated the ball rebounded off the defender's knee and over the bar.
Both sides had chances to win the match in the second half, with Swindon's Evans the busier of the two goalkeepers, first tipping over Sam Sodje's header, before safely collecting Burton's shot.
Sam Parkin's influence on the game grew in the second half, and straight after the restart could have added to his 13 goals for the season but for a last-ditch tackle from Sodje.