Houston (4-2) trailed 45-43 at halftime, but hit six of its first eight shots from the field in the third quarter to take control with a 17-4 run.
Delfino and Chandler Parsons each made four 3-pointers.
Ryan Anderson led New Orleans (3-4) with 23 points, hitting 5 of 7 3-pointers. No. 1 overall draft pick Anthony Davis had 13 points, eight rebounds and three blocked shots, and Greivis Vasquez scored 11 points.
Both teams close out the preseason Friday night. New Orleans will be at Miami, and Houston at Orlando.
Heat assistant coach David Fizdale has moved into the lead in Memphis' fluid search for a new head coach, a source close to the process told ESPN.com on Tuesday night.
In honor of TNT's Craig Sager being announced as the recipient of the Jimmy V Perseverance Award at the 2016 ESPY Awards, look back at NBA coaches and stars paying respect to Sager and disdain to his wardrobe.
TNT reporter Craig Sager will be awarded the Jimmy V Perseverance Award at the 2016 ESPY Awards in July. Sager shares what the award means to him as he has battled leukemia for the past few years.