The 34-year-old Australian – holding the joint record as a four-time Queen’s champion – slipped out to Anderson 6-7 (5/7) 7-5 6-2, after entering the draw on a wildcard.
The 2002 Wimbledon champion is embarking on his last grass court campaign before retiring at the end of the season, and will be dejected to fall at the first hurdle in one of his favourite tournaments.
Hewitt ground his way to the opening set via a tie-break, but was unable to sustain the pace, with big-serving Anderson blasting back to send the match into a decider.
Anderson was then able to close out the clash in reasonably comfortable fashion, despite the three-set affair edging out to two hours and 20 minutes.
Anderson will now face the winner of Tuesday’s keenly-anticipated first-round clash between Nick Kyrgios and French Open champion Stan Wawrinka in his second-round tie.