The Irish province are one of the league's inform sides of late but they were made to work hard for the win, eventually getting the better of Warriors with a 28-25 win.
Leading 21-15 at the break through tries from Noel Reid and Darragh Fanning, plus the reliable boot of Ian Madigan, the hosts were outscored in the second half but still held on for the win, Rhys Ruddock adding a third try.
It moved them above bitter rivals Munster on Saturday night after the former league leaders suffered their first defeat in Wales this season, losing 18-13 at Scarlets.
Trailing by five at the break, the Welsh outfit, who sit sixth in the table, hit back in the second half with John Barclay's try proving the difference between the sides.
Saturday also saw Zebre pick up just their third ever RaboDirect PRO12 victory as they completed the double over Cardiff Blues in Italy.
The reverse fixture had yielded their very first victory and they were back on familiar territory as tries from Brendon Leonard and Giulio Toniolatti earned them a 15-10 win, although they remain bottom of the table.
Benetton Treviso could not complete a pair of Italian wins over the weekend however as they fell to a heavy 38-6 loss at free-scoring Connacht.
John Muldoon was the pick of the bunch, scoring two tries as the bonus point victory saw Connacht make it three straight league wins.
Elsewhere on Friday night, Edinburgh Rugby edged a tight battle with the Ospreys as a double from Grayson Hart handed them a 31-25 win while Ulster Rugby strengthened their grip on third spot with a 38-8 win over Newport Gwent Dragons.
TRY OF THE WEEKEND
There's nothing like turning defence turned into attack and Edinburgh did it with aplomb on Friday night.
With Jack Cuthbert gathering the ball deep in his own defence, he skipped past two tackles before offloading to Sam Beard on Ospreys' 22m line.
The centre then applied the afterburners, sliding in over the line to complete a great counter-attacking move.
BREAK OF THE WEEKEND
There were breaks aplenty in the match between Leinster and Glasgow warriors with Noel Reid catching the headlines early on after evading two tackles to dot down after only six minutes.
But Scotland fly-half Ruaridh Jackson outdid him soon after, throwing a cute dummy to break through the line before powering towards into the Leinster 22 and feeding Richie Vernon to dot down.
Sadly his side could not take the win as well, coming up short by three points.
PLAY OF THE WEEKEND
Despite coming out on the losing side, Ospreys were not short of ideas against Edinburgh, from the conventional to the stylish, as displayed by Justin Tipurics's clever off-load for the game's opening try.
With the Welsh side switching play from left to right with a series of slick passes, Tipuric broke the Edinburgh line near the corner.
Tackled at the death, he still maintained the composure to slip the ball out of the back of his hand and play in winger Jeff Hassler.
PLAYER OF THE WEEKEND
When you've been out for three months, it might be understandable to display a little bit of rustiness.
But that was certainly not the case for Ulster's Tommy Bowe who marked his return from a groin injury in style.
The winger was only handed 40 minutes to ease him back in, but it was still enough time for him to grab two tries and help Ulster to victory over the Dragons.
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