The world number one, who ended the match with a brilliant 106.8 average, had to fight back from 4-1 down to eventually prevail by ten legs to eight.
The 25-year-old will take on Adrian Lewis in Friday’s semi-finals at the Dubai Duty Free Tennis Stadium, where the action takes place outdoors.
“This tournament means a lot to me and it would be fantastic to win it three times in a row,” said van Gerwen, the reigning and defending champion.
“I’m looking forward to my semi-final. The line-up looks brilliant and I’m sure the fans will enjoy a great end to the event.”
van Barneveld started strongly and opened up a three-leg lead in the early stages before ‘Mighty Mike’ began to find some typically devastating form, levelling the match with back-to-back 11-dart-legs and a 13-darter.
‘Barney’ took out 96 but van Gerwen made it five apiece.
He didn’t lead until the 15th leg, when he produced a fabulous 127 finish to break his opponent’s throw.
van Barneveld hit back immediately with an 11-darter of his own but van Gerwen one the last two legs to seal a semi-final spot.