Ulster flanker Chris Henry made some sustained second-half pressure count as last season's Heineken Cup runners-up secured their second win of this season's tournament and condemned Glasgow to a 8-19 loss.
Henry touched down as Ulster drove over after dominating the early stages of the second half in front of a sell-out crowd at Scotstoun.
Peter Horne gave Glasgow the lead in a tight opening half, but Paddy Jackson proved the more competent kicker throughout the contest and Glasgow replacement Niko Matawalu's late try proved only a consolation.
The sides had contrasting opening games with Glasgow 15-0 up at Northampton before falling to a 24-15 defeat, although they were not helped by injuries to Ruaridh Jackson, Stuart Hogg and Sean Lamont.
Only Lamont, with a facial injury, missed out tonight but fellow winger Tommy Seymour was handed a one-week suspension for a tip tackle.
Ulster fielded their influential South African scrum-half Ruan Pienaar with back-row forward Nick Williams also returning after last week's bonus point win against Castres.
The 6,194 fans, including a large away contingent, were welcomed by torrential rain and the conditions contributed to a scrappy opening with neither side able to get much momentum.
Ulster had two early chances with penalties from inside their own half but Jackson and half-back partner Pienaar were narrowly wide and just short respectively.
Warriors, who have won their last four RaboDirect Pro12 games after losing to Ulster in the opening week, got two chances of their own from around 35 metres after scrum offences and Horne opened the scores with his second effort.
Jackson soon levelled with a 20-metre penalty after Glasgow were penalised for holding on. Some slack play in their own 22 saw Glasgow remain under pressure and Jackson put the visitors ahead just before the half-hour mark with another penalty from a similar distance.
Glasgow were forced into two substitutions before the break with flanker Chris Fusaro and winger Byron McGuigan going off through injury and Jon Barclay and Niko Matawalu coming on.
Glasgow's scrummaging allowed them to briefly put Ulster under pressure but Horne missed a good penalty chance and, with the conditions easing, Ulster threatened to extend their lead.
Pienaar's delicate kick put Glasgow under serious pressure but a knock-on eventually let the hosts off the hook.
Horne was given another chance moments after the restart after another scrum offence but was wide from just inside the Ulster half.
That proved the centre's last contribution before he went off with apparent concussion with Scott Wight coming on and Hogg moving from full-back.
The rain had totally subsided but Glasgow could not shake off the errors and stand-off Jackson gifted possession to Ulster near the halfway line, with the visitors gradually working their way towards the five-metre line.
Some desperate defending repelled them but the respite was brief and Ulster were back in the danger zone when Tommy Bowe bundled Hogg into touch, but some poor handling by the winger soon let Glasgow off the hook.
Barclay again replaced Fusaro, who had reappeared for the second half, and Rob Harley returned from a knee injury as Glasgow tried to ease the pressure.
They could only do so briefly and Pienaar was just short with a penalty from near the halfway line.
Ulster's Jackson soon decided to kick for touch with another penalty closer in but near the touchline, an award which left the home side confused, and the visitors soon drove over after the lineout with flanker Henry touching down amid a plethora of bodies in the maul.
Jackson converted and soon extended the lead to 13 points with 18 minutes to play with another penalty following a rare scrum offence from the hosts.
Wight's kick put the visitors on the back foot, but Jackson's attempted kick through Ulster's back line was intercepted and the visiting Jackson kicked another penalty in his last act.
Glasgow rallied in the final stages and Matawalu touched down after Wight's crossfield kick after an enterprising run by Ryan Wilson was halted near the try line.