But the Scots had Bernardo Stortoni sin-binned as Munster pummelled the visitors' try-line late on, and O'Gara mopped up with the match-winning penalty.
O'Gara had a key contribution for the home side, kicking five penalties and converting David Wallace's second half try.
Colin Gregor and DTH van der Merwe scored tries in either half for the Warriors, and young out-half Jackson finished with an eight-point haul.
The narrow victory keeps Munster nine points clear at the top of the table, while Glasgow, who watched Jackson miss a late, long range drop goal, slip to tenth.
Jackson's seventh-minute penalty opened the scoring after O'Gara had a kick charged down and John Hayes was pinged for not rolling away after a tackle.
Munster, who brought Denis Hurley in for the injured Doug Howlett (calf) as a late change, mounted a swift response.
Paul Warwick attacked with vigour and his kick forward was deflected into the path of Johne Murphy, who was brought to ground close to the Glasgow posts. Richie Gray killed the ball at the ensuing ruck and was promptly yellow carded by referee James Jones.
O'Gara tapped over the penalty to level the tie, but Munster could not make use of their numerical advantage.
Jackson missed a kickable penalty from the left, before Munster's forwards began to exert more influence, and it took a terrific turnover from Ryan Grant to release the pressure on the Warriors.
Munster's frustration grew as infringements in the scrum and at the breakdown cost them valuable possession and territory, and Glasgow caught them off guard in the 37th minute.
Max Evans broke out of a double tackle near the Munster 22 and although Warwick caught up with him, his well-weighted pass inside was carried on by scrum half Gregor whose fast feet saw him glide in behind the posts for a converted try.
On the stroke of half-time, Munster were pressing for a score when Keith Earls was very harshly sin-binned for not coming through the gate at a ruck.
Munster had got on the wrong side of referee Jones in the opening half, but they quickly turned the 10-3 interval deficit around.
They stormed out of the blocks for the second half, with O'Gara landing a quick hat-trick of penalties. The game lulled along towards the hour mark, with Murphy, van der Merwe and Evans providing some spark with ball in hand.
Jones did well to spot Wallace's grounding for his 62nd minute try, following a series of close range surges from the Munster pack. O'Gara's conversion gave the men in red some breathing space at 19-10.
However, Glasgow, hunting for their first away win of the season, had other ideas. Jackson was involved twice and Evans did brilliantly to pass out of the tackle, before the former unleashed van der Merwe for his seventh try of the league campaign.
Gregor stepped in to add the conversion and three minutes later, Jackson followed up with a tidy drop goal. Suddenly, a repeat of the Warriors' 2008 win at this venue was on the cards.
Yet Munster had time on their side and although their try-scoring attempts were thwarted - Stortoni saw yellow for deliberating knocking on, with the hosts about to convert an overlap - O'Gara was able to fire over his sixth successful kick from six attempts to keep the province on the winning trail.
|Munster Rugby Score Card|
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|