Matthew Crossan played a neat cross-field ball to Barry Curran in space on the right hand side of the penalty box and the Ballindrait man made no mistake firing low across Alan Gough into the far corner of the net.
After this, it was the hosts who had the better of the goal-mouth action in the first period, forcing a succession of corners, which kept Harps ‘keeper James Gallagher on his toes.
Fran Carter watch his shot from 18 yards held by Gallagher while Alan Murphy rounded Gallagher only to have his final effort cleared by Jonathan Minnock after a mistake from Eloka Asokhu.
Barry Moran also had a noteworthy opportunity of levelling the tie ten minutes from the half-time whistle, but he headed wide after Ronan Frawley flicked Alan Murphy's corner into his path.
At the other end, Harps carved out a great chance of doubling their advantage, but Matthew Crossan shot over after a neat attacking move involving Walsh and Malseed.
Galway got back on level terms on 66 minutes when they were awarded a penalty following a foul by Sean Mc Gowan on Derek O'Brien.
Up stepped former Derry City player Alan Murphy to send James Gallagher the wrong way for his third penalty success in a week having converted two spot-kicks against Limerick midweek
With 15 minutes remaining on the clock, Harps were reduced to ten men when Stephen O'Donnell was shown a straight red card for appearing to kick out at Galway centre-back Wesley Charles.
In a nervy conclusion, Galway laid siege on the Harps goal and came within inches of edging themselves into the lead, but Ciaran Foley smacked the crossbar from inside the box.
Moments earlier, Donegal man Mick O'Donnell came close to getting on the scoresheet, but he was denied by Gallagher at his near post and deep into stoppage time Alan Keane had an effort come off Gallagher's crossbar.
This was certainly a vital point for what is a rejuvenated Harps outfit who now look forward to two home games in a row.
Galway United: Alan Gough; Alan Keane, Mick O'Donnell, Wes Charles, Ronan Frawley; Fran Carter, David Cooke, Michael Harty, Derek O'Brien; Barry Moran, Alan Murphy. Subs: Ciaran Foley (for David Cooke, h/t); David O'Dowd (for Barry Moran, 68); Nigel Keady (for O'Brien, 73).
Finn Harps: James Gallagher; Sean Mc Gowan, David Bell, Jonathan Minnock, Eloka Asokhu; Chris Malseed, Michael Funston, Matthew Crossan, Barry Curran, Stephen O'Donnell; Davitt Walsh. Subs: Anthony Gorman (for Walsh, 73).
Referee: Neil Doyle (Dublin).
Finn Harps Dot Com Man-of-the-Match: Harps had quite a few contenders for this award tonight, with Jonathan Minnock putting in an excellent evening at the office to mark his 400 th appearance for the club.
The midfield pairing of Malseed and Funston, though, was sublime with Malseed just shading the award for putting in immense work and graft from the middle.
The fair-haired Letterkenny man will be a key asset for Harps in the coming weeks and months and if he can replicate this performance, Harps will be hard to stop.