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 will play fourth-seeded Jo-Wilfried Tsonga in a repeat of the 2011 final. The Frenchman ended the run of 112th-ranked American Denis Kudla, 6-3, 6-2 in 53 minutes.
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.