McDowell reached the quarter-finals of this event on his debut in 2011, the final in 2012 and won the title last year, while his victory over Alexander Levy in the opening group match on Wednesday made for an overall record of 15 wins from 17 matches.
However, the former US Open champion found Mikko Ilonen in brilliant form at The London Club, the Finn carding seven birdies to hold off a determined McDowell fightback and secure a 2&1 win.
Both players found a greenside bunker at the short 17th but after McDowell missed his birdie attempt from long range, Ilonen holed out for birdie to seal the win.
“I’m disappointed to lose but Mikko was incredibly solid,” McDowell said. “I felt like I played the best golf the first five holes but he putted better.”
Gallacher managed six birdies of his own against Pablo Larrazabal, but saw the Spaniard hole a pitch from 30 yards on the 18th to snatch an unlikely victory.
“I was five under today and have played two guys that haven’t had any bogeys,” said Gallacher, who lost to Ireland’s Shane Lowry in his opening group match and cannot qualify for tomorrow’s quarter-finals.
Dubuisson saw off Offaly man Lowry 3&2. Four down with six to play, Lowry had kept his hopes alive by also making a birdie on the 13th but remained three down with three to play. Dubuisson duly completed a 3&2 win to make it two wins out of two, a feat matched by Joost Luiten with a commanding 4&3 victory over Alexander Levy.
All four members of the Larson Group can still qualify for the quarter-finals.
The best golf of the day came from Sweden’s Henrik Stenson, who recovered from three down after four and was eight under par for his last nine holes in beating Francesco Molinari 2&1.
Stenson tops the Palmer group with three points ahead of George Coetzee and Thongchai Jaidee&.
All four players in the McCormack Group have two points after Jamie Donaldson beat Jonas Blixt 3&2 and Patrick Reed defeated Paul Casey 2&1.