Wingers Michael Allen and Craig Gilroy scored Ulster's tries as they held off a determined Glasgow in Friday's opening Pro12 match at Ravenhill.
After Ulster replacement and Niall O'Connor and Glasgow's Duncan Weir had exchanged penalties, Allen got in for a try on the left just before half-time.
Gilroy broke away for an intercept try early in the second just as Glasgow were pushing for a score.
Former Ulster player Tommy Seymour scored a 68th-minute try for Glasgow.
That cut Ulster's lead to 15-10 and O'Connor settled the home nerves with a late penalty.
The sides will meet next in the Heineken Cup - at Glasgow new Scotstoun Stadium base on 19 October.
Friday's Belfast match was Ulster's first competitive outing under new coach Mark Anscombe and he will have been relieved to get the win as Glasgow were right in it until O'Connor's late penalty made the gap eight points.
O'Connor, back at Ravenhill after a spell with Connacht, had come on when number 10 Paddy Jackson hobbled off with an injury.
The replacement fly-half's first duty was to slot over the opening penalty after hooker Finlay Gillies had been deemed guilty of coming in from the side.
Glasgow drew level 10 minutes later with a Weir penalty after Nick Williams was penalised at the breakdown.
Ulster then came close when Nick Williams lost control when crossing the line and then O'Connor hit an upright with a 27th-minute penalty.
The fly-half then missed again with a good chance on the half-hour but Ulster responded and a driving charge for the line resulted in Glasgow winger Tommy Seymour being sin-binned for dragging the maul down.
The result was a series of scrums near Glasgow's line and, after being held up five yards short in front of the posts, scrum-half Michael Heaney fed Jared Payne whose fine long pass put Allen in.
Ulster, 8-3 up, started the second half in perfect fashion when Gilroy intercepted Weir's pass and ran all the way in under the posts from just outside his own 22, with O'Connor this time making no mistake with the extras to put Ulster 15-3 up.
Glasgow replacement Ruaridh Jackson's 63rd-minute penalty hit an upright but then, on a rare attack, Jackson worked Seymour clear and the winger rounded two defenders to score before Jackson added the conversion to narrow Ulster's lead to 15-10.
Ulster were then unable to build on their lead when O'Connor was again wide with a 72nd-minute penalty attempt but did hit one in the last minute.
Ulster: Payne, Allen, Farrell, L Marshall, Gilroy, Jackson, Heaney, Black, Herring, Afoa, Muller, Stevenson, Diack, Doyle, Williams.
Replacements: Brady, Court, Fitzpatrick, McComb, McComish, P Marshall, O'Connor, Cave.
Glasgow: Murchie, Seymour, Dunbar, Morrison, S Lamont, Weir, H Pyrgos, Reid, Gillies, Cusack, Ryder, Kellock, Harley, Fusaro, Wilson.
Replacements: Hall, Low, Grant, Eddie, Barclay, Cusiter, Jackson, Horne.
Referee: Marius Mitrea (Italy)