The Warriors are the only team to have won each of their opening three fixtures, although they had to come from behind to maintain their 100 per cent record having trailed 19-14 at the interval.
Glasgow scored seven tries in total, all of which were converted by Hastings, who was the first Warriors player to cross and also booted over a penalty in a fine all-round display.
Tommy Seymour, D.T.H. van der Merwe, Callum Gibbins and George Horne were the others to go over for a Glasgow side that took advantage of Malcolm Jaer's yellow card early in the second half.
Leinster also scored seven tries as the returning Johnny Sexton and Rob Kearney helped it overcome the Dragons 52-10.
Of those points, 35 were scored in the second half, with scum-half Jamison Gibson-Park contributing two tries.
Cardiff Blues threw away a three-try lead as Zebre claimed a dramatic 26-24 victory to leave the Welsh side still winless.
Olly Robinson, Kristian Dacey and Gareth Anscombe all touched down inside the first 11 minutes and Zebre only went ahead for the first time all night when Oliviero Fabiani crossed in the final stages.
The Scarlets handed Benetton Treviso its first defeat of the campaign, with a 38-29 success that was achieved against a team which played with a one-man disadvantage for nearly an hour.