Danny North's 77th minute saw St Pat's climb above Bray in the Premier Division after their third win on the spin.
The result brought an end to the Wicklow team's five match unbeaten run and saw them lose at the Carlisle Grounds in their 800th League of Ireland fixture.
North claimed his fourth league goal of the season when converting Ian Bermingham's low cross from the end-line.
There was a controversial ending to the match as Adam Mitchell when sent off by referee Alan Kelly after clashing with Bermingham in injury time.
|11||St. Patrick's Athletic||19||16|
|12||Galway United FC||19||15|