The Dutchman, 27, raced into a 3-0 lead and a whitewash looked likely but 45-year-old Scot Anderson fought back to take the fourth and sixth sets.
Van Gerwen, who won the title in 2012 and 2014, then closed out the match.
He wrapped up the win with a 160 check out on double 20 and the £100,000 prize money to seal a 5-2 victory.
"This is my third one and I played fantastic all week so it's great to go on and win the trophy," Van Gerwen told Sky Sports.
"I averaged 106 or 107 in the early sets and if you play like that you deserve to win the trophy. Gary pushed me to the end and never gives up."
Michael van Gerwen brushed aside Gary Anderson in the World Grand Prix final in Dublin to win the tournament for the third time in his career.