TURIN, August 30, 2014 (AFP) - That left him in sixth place going into the final day, six strokes back off tournament leader South Africa's Hennie Otto and crucially four behind fellow Scot Richie Ramsey in second place.
Austria's Bernd Wiesberger is third on 13 under after following consecutive rounds of 66 with a 71, with English duo Lee Slattery and Ross Fisher sharing fourth on 11 under.
The 39-year-old Gallacher arrived in Italy knowing that he needed to place first or second in the final qualifying tournament for the Ryder Cup, being held at Gleneagles near his home in late September, to dislodge Graeme McDowell from the ninth and final automatic spot in Paul McGinley's 12-strong team.
The Irishman after that has three wildcard picks at his disposal which he will announce on Tuesday.
With such as Luke Donald, Ian Poulter and Lee Westwood looking for wildcard picks, Gallacher knows that he is up against it hence his desparation to catch the eye in Turin.
"It keeps me in touching distance," Gallacher said of his round.
"The worst thing I could have done was open up a big gap which was insurmountable. I've not done that so a good day on Sunday and I am still right in there. I had about four lip-outs today but they went in on Friday and I holed a couple of good putts at the end so it evens itself out.
"It's all to play for. You never know what happens in this game and guys have won from further back than this. I'll just go out and try and get as many birdies as possible and see what happens.
Gallacher admitted he was focused on second place after Otto's 62 on Friday, but first place was back on the agenda after the ninth hole.
Otto had to take a penalty drop after carving his second shot into the trees and could only find a greenside bunker with his fourth shot, leading to a double-bogey seven.
The 38-year-old responded with a birdie from six feet on the 10th as Wiesberger dropped his first shot of the week on the same hole, with Ramsay moving into second on 13 under thanks to a two-putt birdie on the 12th.
Gallacher chipped to five feet for a birdie on the par-five 15th and at 10 under was three behind Ramsay in a tie for fifth.
Gallacher parred his final three holes to complete a 69 and finish 10 under, four behind Ramsay who occupied second place after holing from 40 feet on the 18th to card a flawless 66.
"I would hate to be the person to deny him a place on the Ryder Cup but I know if it comes down to it he plays to win and that's the same attitude I have to have," Ramsay said.
Collated third round scores in the Italian Open at Circolo GC on Saturday (par 72) (x denotes amateur, GBR unless stated):
200 - Hennie Otto (RSA) 67 62 71
202 - Richie Ramsay 67 69 66
203 - Bernd Wiesberger (AUT) 66 66 71
205 - Ross Fisher 69 66 70, Lee Slattery 70 68 67
206 - Stephen Gallacher 72 65 69
207 - Francesco Molinari (ITA) 66 72 69, Joost Luiten (NED) 69 68 70, David Howell 73 67 67, Shiv Shankar Prasad Chowrasia (IND) 69 72 66
208 - Carlos Del Moral (ESP) 70 68 70, Ricardo Gonzalez (ARG) 74 66 68, Marc Warren 69 70 69, Romain Wattel (FRA) 73 68 67, Andrew Sullivan 70 72 66, Mikko Korhonen (FIN) 70 67 71, Darren Fichardt (RSA) 68 69 71, Simon Dyson 71 68 69, James Morrison 70 66 72
209 - Richard Bland 67 71 71, Merrick Bremner (RSA) 71 68 70, Edoardo Raffaele Lipparelli (x) (ITA) 68 70 71, Soren Hansen (DEN) 71 66 72, Morten Orum Madsen (DEN) 68 68 73, Daan Huizing (NED) 69 71 69, Francesco Laporta (ITA) 68 72 69, Darren Clarke 72 70 67, Seve Benson 70 67 72, Tommy Fleetwood 72 70 67, David Lipsky (USA) 69 67 73, Andreas Harto (DEN) 70 69 70, Alexander Levy (FRA) 73 68 68