The 21-year-old from Norwich edged a tight first set after a tie-break out on Court 11.
He led 4-1 in the second set but was pegged back by Houdet before taking another tie-break to complete a 7-6 (9) 7-6 (5) victory.
Hewett said: “I was disappointed to not be on a bigger court, but I’ve never lost on this court so thank you to whoever made that decision.
“Thanks to everyone back home, it’s great to win and to defend the title.”
Hewett claimed another title in the doubles with Scotland’s Gordon Reid, the British duo coming from a set down to beat Gustavo Fernandez and Shingo Kunieda 11-9 in a match tie-break.
Meanwhile, Eastcote’s Andy Lapthorne won the wheelchair quad singles with a comprehensive victory over Dylan Alcott. Lapthorne, who lost to Australian Alcott in this year’s Wimbledon final, won 6-1 6-0 in just 56 minutes to add to his 2014 US Open triumph.
Lapthorne and Alcott then linked up to win the doubles final, 6-7 (5) 6-1 10-6 after a match tie-break against American pair Bryan Barton and David Wagner.