Ulster came flying out the blocks and were on the board with less than a minute on the clock.
Scrum-half Isaac Boss sent a testing chip into the host's 22 that was eventually collected by Rory Lamont but his team-mates were penalised for entering the ruck illegally from the side.
Humphreys opened the scoring with the resulting penalty but Glasgow almost replied with a try soon after but centre Andy Henderson;'s pass to Hefin O'Hare was ruled as forward.
The first try of the game occured when Colin Shaw was penalised for an early tackle from which Ulster surged into the 22 before before Boss produced a smart dummy before touching down.
Humphreys converted but Glasgow responed with a penalty from the boot of Dan Parks that was set up by a powerful burst by Andy Henderson.
The Humphreys thumped over a long-range penalty after Warriors hooker Scott Lawson was warned for dissent and things got worse for the home side when lock Justin Harrison grabbed Ulster's second touchdown.
Humphreys slotted another penalty before the Scots rallied with a try from replacement Johnny Beattie.
Parks traded penalties with Humphreys before Beattie set up another score for O'Hare that Parks converted to ensure a tense finale.
However any hope of a late comeback were denied when Humphreys slotted over his fifth and final penalty.
|Glasgow Warriors Score Card|
|Ulster Rugby Score Card|