Early on Ulster’s Henderson hurtled through t he short-handed home defence for the touchdown. Jackson added the extra two points.
On 22 minutes the hosts capitalised on a spell of sustained pressure when Russell steered a penalty between the sticks to open the home side’s account.
The Scots trimmed the deficit to a single point when Russell booted his second penalty of the evening after 28 minutes.
Against the run of play, Ulster extended their lead five minutes before the interval when Jackson slotted a three-pointer.
Glasgow bounced back and, with the clock ticking towards half-time, earned a penalty within the range of Russell who added a further three points to his tally, leaving the hosts one point adrift at the interval, trailing 10-9.
On the resumption the visitors were next on the scoreboard in bizarre circumstances. Although appearing to take the kick from the wrong spot, Pienaar booted a penalty award into touch 10 metres from the Glasgow line and with the home defenders strolling back, Craig Gilroy took a quick throw to McCloskey who jogged in. Jackson thumped over the conversion.
Then on 56 minutes Hogg won the race to the line, despite the attentions of Pienaar.
Glasgow snatched the lead with 18 minutes to play after another scintillating contribution by Russell, who delivered a pinpoint cross-kick to Seymour, and the winger blazed past two defenders to touch down. Russell’s conversion scraped over to hand Glasgow a four-point advantage.
That grew to seven points after 73 minutes when Russell added another penalty. And although the Scotland stand-off missed with a kick at goal that would have left Ulster empty-handed, Hogg robbed the visitors of the consolation point when he hammered over a penalty from inside his own half to add gloss to the win.
Tries: Hogg, Seymour. Cons: Russell. Pens: Russell 4, Hogg.
Hogg, Seymour, Bennett, Dunbar, Lamont, Russell, Pyrgos, Reid, Brown, Puafisi, Gray, Nakarawa, Harley, Fusaro, Strauss.
Hart for Pyrgos (66), Yanuyanutawa for Reid (69), Malcolm for Brown (69), Fagerson for Puafisi (69), Wilson for Fusaro (23), Swinson for Strauss (63).
Tries: Henderson, McCloskey. Cons: Jackson 2. Pens: Jackson.
Olding, Gilroy, L. Marshall, McCloskey, Scholes, Jackson, Pienaar, Black, Herring, Lutton, O’Connor, van der Merwe, Henderson, Henry, Williams.
Cave for Scholes (75), P. Marshall for Pienaar (75), McCall for Black (63), Warwick for Lutton (75), Diack for O’Connor (27), Reidy for Williams (41).
John Lacey (Ireland).
Cardiff Blues 56 Benetton Treviso 8