The top-seeded Murray served eight aces without a double-fault, and broke twice in each set. He also dropped serve three times in the match, but dominated the tiebreaker by winning the first six points.
Murray looks forward to the challenge of playing Tsonga, who reached the semifinals of the French Open.
"It will be a big step up and also a really big test for me because he's been playing some great tennis the last couple of months," Murray said. "He's one of the best in the world on this surface. I have had some tough matches with him on grass before, so tomorrow will be the same."
Hewitt took a 4-2 lead with a backhand winner after del Potro struck consecutive double-faults, and hit a backhand volley to break again for the set.
Del Potro sped to a 4-0 lead in winning the second set. In the decider, Hewitt broke del Potro at love to earn a 3-1 lead and broke again at 5-2 with a volley winner.