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Magners League newcomer Ruan Pienaar scored all of the points as Ulster scraped to their fourth win of the campaign, finding a way past a gutsy Glasgow side at Ravenhill.
Pienaar made an immediate impact for Ulster as he chalked up an impressive tally of 19 points, including the match-winning penalty in the 72nd minute.
There was a huge sense of anticipation as the Springbok star made his bow in front of an expectant Ravenhill crowd and although he missed three kicks at goal, the 26-year-old was a key figure throughout the game.
Glasgow, who did the double over Ulster last season, were hoping to end a run of three successive defeats. Their teenage out-half Duncan Weir booted them ahead in Belfast and Canadian winger DTH van der Merwe caught the hosts out with an opportunist 11th minute try.
Pienaar then took centre stage, scoring 13 points in a lively nine-minute spell to nudge Ulster in front for the first time. As the Ulster forwards gained ground, captain Rory Best passed from the back of a maul for Pienaar to get over in the right corner past Glasgow's Colin Gregor.
Weir threaded over three penalties, either side of half-time, to give the Warriors real hope. The Scotland Under-20 international landed a monster score in the 50th minute to move his side back in front at 17-16.
But Pienaar's fifth successful kick at goal decided this closely-fought affair, with the result extending Ulster's unbeaten run to five matches.
Speaking afterwards, Ulster coach Brian McLaughlin expressed his satisfaction with the result but not the level of performance.
"We knew it was going to be very competitive and the match turned out to be very tight, Glasgow pushed us hard," he acknowledged.
"We're happy with the result but we still have a fair bit to go in terms of performance as we are making too many basic errors.
"We need to hold onto the ball and have to push away from sides when we get our noses in front. It's good to get the results but we want to play quality rugby."
Glasgow coach Sean Lineen fielded an unchanged team from last weekend's home defeat to Munster. Amongst the replacements, Pat MacArthur, Ryan Grant, Aly Muldowney and former Ulster centre Rob Dewey earned recalls to the matchday squad.
Fresh from a 15-15 draw with their provincial rivals Connacht, the Ulstermen brought Pienaar, Niall O'Connor and the fit-again Simon Danielli into their back-line.
Team captain Best made his 100th competitive appearance for Ulster in the front row, while recent Ireland cap Dan Tuohy and South African duo Johann Muller and Robbie Diack were restored to the pack.
Pienaar missed a penalty attempt from inside his half as Ulster looked to settle, leaving Weir to open the scoring after Bryan Young was penalised for not rolling away after the tackle.
The Warriors number 10 was prominent in the early stages as Glasgow took the game to the hosts, with Jon Welsh, Robert Harley and skipper John Barclay the pick of the forwards.
From a slightly miscued Weir kick, Ulster winger Andrew Trimble failed to gather the high ball close to the halfway line. Glasgow turned defence into attack immediately, as Max Evans popped the ball to van der Merwe who had the pace to make it over in the left corner, catching Ulster out of position.
Weir's unsuccessful conversion attempt was followed by a penalty brace from Pienaar, his first kick clipping the left hand post before going over.
Ulster were beginning to find some rhythm. Glasgow's defence held them at bay, before a forceful lineout maul gave Best the chance to link with Pienaar on the blindside and he brushed off Gregor's tackle to make the try-line.
Pienaar followed up with a superb conversion from wide out on the right, and there was a growing sense that Ulster were about to pull away.
However, Glasgow had the better of play in the lead-up to half-time. Weir, who was off target with a drop goal attempt, landed his second penalty to punish Tuohy for taking out Federico Martin Aramburu.
Evans popped up on Graeme Morrison's shoulder to take a pass and race towards the Ulster posts, but Morrison's delivery was ruled forward.
Yet, Glasgow did well to retain possession in the closing stages, with their forwards making the hard yards. They drew a penalty for a ruck offence from Diack in the Ulster 22, and Weir kicked his side to a 14-13 half-time lead.
Ulster had a real fight on their hands and although Pienaar restored the hosts' advantage, courtesy of a 45th minute kick which was helped through by the crossbar, McLaughlin's men could not pull away on the scoreboard.
Glasgow hit back with a stunning 60-metre penalty from the nerveless Weir, who was making just his second league start. With a distinct lack of try-scoring chances, the game turned into a shootout between the place-kickers.
Pienaar missed a kickable penalty from the right, after Glasgow number 8 Richie Vernon had taken out Trimble as he chased his own kick through. Weir then tried his luck from 65 metres and admirably had the distance but not the accuracy, with his kick slightly to the left of the target.
But Ulster enjoyed enough dominance in the final quarter, forcing Glasgow back on the defensive for the most part, to seal another four-point return. Pienaar had two penalty opportunities in the closing eight minutes, the first of which he nailed.
Glasgow could not get back within scoring range, despite an influx of fresh legs, and the losing bonus point was their only reward for a gallant display.