Tries from Joe Simpson, Tom Varndell, Ben Jacobs and Dominic Waldouck helped the Aviva Premiership club climb to second place, two points behind leaders Toulouse.
Hanks had identified Glasgow as a must-win match and was delighted with the response from his side.
"It puts us in a better position in the pool. This was a huge game that we had to win to stay in the pool," said Wasps’ rugby director.
Wasps scorers: Tries: Simpson, Varndell, Jacobs, Waldouck. Cons: Walder 3. Pens: Walder 4.
WASPS: Haughton, Varndell, Jacobs, Flutey, Lemi, Walder, Simpson, Beech, Webber, Taulafo, Shaw, Birkett, Ward-Smith, Betsen Tchoua, Powell.
Replacements: van Gisbergen for Haughton (41), Waldouck for Jacobs (46), Ward for Webber (61), Broster for Taulafo (64), Worsley for Shaw (64), Veale for Birkett (77).
Glasgow scorers: Tries: Jackson, Hall. Cons: Harley, Jackson. Pens: Jackson 4. Glasgow: Stortoni, van der Merwe, M. Evans, Morrison, Aramburu, Jackson, Gregor, Welsh, Thomson, Low, Ryder, Gray, Harley, Barclay, Vernon.
Replacements: Pyrgos for Stortoni (60), Dewey for Aramburu (46), Grant for Welsh (64), Hall for Thomson (41), Kalman for Low (57), Forrester for Ryder (57), Wilson for Vernon (70).