Bradley's free kick, his first league goal of the season, came after an identical effort was spectacularly pushed behind by Barry Ryan only moments earlier. But Ryan could do nothing when Bradley's second effort wrong-footed him and despite getting a hand to the ball, Ryan couldn't prevent the ball nestling in the top corner. The win moves Rovers to within four points of Bohemians, but the result was slightly harsh on a Galway side who been reduced to ten men before the contest had reached half time.
Both sides made switches to their starting line-ups, with Galway giving Aaron Greene his first start and recalling David Cooke to the midfield. The Hoops brought in Ian Bermingham after an injury lay-off, while Shane Robinson replaced Paddy Kavanagh, Aidan Price came in for Darragh Maguire and recent signing Graham Barrett had to, unsurprisingly, make do with a spot on the bench.
The supposed divide in class between the sides was unapparent in the opening half as Galway traded on parity for much of it before seeing their centre half sent off six minutes before the break following an incident with Dessie Baker. Moments earlier, Guthrie had cleaned out Baker with a committed challenge on half way and when the visitors received an attacking free kick on the right hand side, another tamer exchange between the two evolved with Baker crumpling to the floor on the edge of the area and Buttimer singling out the Kerryman for an early bath.
The cards suddenly stacked in Rovers favour, Sean Kelly reverted to centre half and Alan Murphy dropped into midfield after an encouraging display from the former talisman. Favouring a more attacking strategy than anticipated, Ian Foster had partnered Murphy with young Greene, while the narrow United quartet in midfield worked doggedly to frustrate the Tallaght-based side.
Chances were few and far between in the first 45, with Shane Robinson's shot eliciting the only save of the half from United's Barry Ryan. Cooke and Mark O'Toole, an early substitute for Iarfhlaith Davoren, got a couple of testing deliveries into the area but a telling finish was not at hand on either occasion. Greene headed wide and had possibly the best opportunity of the half blocked by a brilliant cover challenge from Pat Sullivan, who spent the rest of the game modelling a large white bandage on his head for his trouble.
Rovers struggled to find an rhythm for large parts of the half, but were then handed the initiative when Baker conned Buttimer into a decision which ultimately cost the home side any chance of grabbing some "bonus points", as Foster had previously described games with the Top Four.
Screaming out of the blocks in the second half after presumably being on the receiving end of some stern words from Michael O'Neill, Rovers went close to opening the scoring twice within the opening few minutes. First, Stephen Rice turned sharply in the box but was denied by Garry Breen's intervention, before Gary Twigg rattled the bar with a close range header. An onslaught was envisaged, but to the home side's credit they battled admirably over the next fifteen minutes.
The fighting spirit enlivened the home fans and their team responded by driving forward down the flanks; Cian McBrien's shot and some teasing crosses from Cooke provided signs of an unlikely breakthrough, which eventually, inevitably, went the Hoops way on 74 minutes.
By that time, Barrett and Ollie Cahill had both been sprung from the bench as a sign of O'Neill's growing discontent with his side's efforts. While their efforts did improve, it took some dead ball magic to snatch all three points. The late sending off of Pat Sullivan for a second yellow card, ironically named as TG4's Man of the Match as he departed the field, made no difference to the final outcome, as hard as the home side toiled to level matters.
Not for the first time in his career, the name of Anthony Buttimer was upmost in a lot fans' thoughts as they departed the ground, and a chorus of boos greeted the Cork official's final whistle which extended Rover's unbeaten league run to sixteen.
Galway United: Barry Ryan; Seamus Conneely, Garry Breen, Shane Guthrie, Iarfhlaith Davoren (Mark O'Toole, 14); Cian McBrien (Jason Molloy, 82), Sean Kelly, John Russell, Dave Cooke; Alan Murphy, Aaron Greene (Vinny Faherty, 71).
Subs not used: Ger Hanley, Paul Sinnott.
Shamrock Rovers: Alan Mannus; Ian Bermingham, Craig Sives, Aidan Price, Pat Sullivan; Sean O'Connor, Stephen Rice, Stephen Bradley, Shane Robinson (Ollie Cahill, 67); Dessie Baker (Pat Flynn, 94), Gary Twigg (Graham Barrett, 67).
Subs not used: Barry Murphy, Ross Chisholm.
extratime.ie Man of the Match: Stephen Bradley.
Referee: Anthony Buttimer.