Scrum-half Pienaar scored all of Ulster's points in the 22-19 win over the Tigers at Welford Road and the 1999 champions will now play Saracens in the last eight at Ravenhill in April.
Piennaar not only kicked five penalties and a conversion but also scored the crucial try after charging down a clearance from Leicester fly-half Toby Flood in the 58th minute to level the scores at 19-19.
His winning penalty, in the 69th minute, was from a metre inside his own half, his second monster kick of the game.
Muller said: "It seems like it's happening every week, when he scores all the points.
"I came here with him yesterday to do kicking practice and he did not miss one all day. He was outstanding and kicked them from 60, 62 metres. From a captain's point of view it gives you a lot of confidence.
"A huge amount of credit to him and it doesn't just happen. He puts a huge amount of work in, he puts hours and hours into his kicking and it's wonderful when it pays off."
Ulster's win means they top Pool Five with six wins out of six and in April will have a chance to avenge last season's quarter-final defeat at Saracens.
This time, however, they will have home advantage, and Muller said: "We came here to get a home quarter-final.
"Sarries totally outplayed us last season. They are a great side and don't mind going away to get a result.
"It's two months away and at this stage we will just enjoy the moment. We have not achieved anything yet and there's a huge amount of work left if we are to achieve something."
Leicester led 19-9 after a 49th-minute try by winger Niall Morris had put them in the driving seat.
But Flood, who converted the try and kicked four penalties out of five, cost Leicester dear when his clearance was charged down by Pienaar nine minutes later.
Richard Cockerill, Tigers' director of rugby, said: "We're disappointed with the result, but it was a good game.
"It was very tight margins and we dropped the wrong side of those margins. Ten points up, we needed to control the game better but we did not manage the back field as well as we would have liked and they exposed us.
"To lose to a charge-down kick is disappointing but you make your own luck.
"I am not going to criticise us. The luck of the draw fell their way tonight and that happens in sport. It wasn't for a lack of effort. We played some good stuff and you just have to take it on the chin."
Leicester, who suffered their first home defeat in the competition since 2006-2007, face a quarter-final away to a French team, either Toulon or Clermont Auvergne, and should have their England and British Lions pair Manu Tuilagi and Geoff Parling back by then.
"At the moment it's probably Toulon, tomorrow it may be Clermont who have an average home record, what is it, 73 games unbeaten," said Cockerill.
"We are in the quarter-finals and we have suffered a lot of adversity (through injuries), so that's not a bad effort from us."
- Sports & Recreation