Nick Williams has recovered from a rib injury picked up in the RaboDirect PRO12 win over Connacht a fortnight ago and will start the game at number 8 in place of Mike McComish who is named on the bench.
Ruan Pienaar showed his class in scoring the vital bonus point try as a replacement against Castres Olympique and will start at scrum half this time.
Paul Marshall, who had ably deputised for the Springbok in recent weeks, scored two tries in a man-of-the-match display against the French side, highlighting Ulster's strength in depth in the position.
Indeed, Anscombe admitted it was a tough decision regarding who should wear the number 9 jersey on Friday night.
"Paul played outstandingly well last week and he showed what he is capable of with a man-of-the-match performance," he said.
"But we're in the position where we have two fantastic options at scrum half. Ruan came on and showed what a quality player he is with his distribution and the try and the end.
"We have to select the team to win specific games and that's what we've done for this weekend. Rugby is an 80-minute game and it's important to have someone like Paul, who can come on and make an impact."
The Ulster boss is also pleased to have back rower Williams available again, adding: "Nick has trained all week and has proved that he is 100% fit. He's looked sharp and it is good to have him back in the team."
Anscombe's reign at Ulster has been characterised by squad rotation but there has been a more settled look about the team in recent weeks.
He commented: "We're getting more and more players back from injury and it is allowing us to get close to a full strength team. We now just have a couple of players missing, so it's looking quite promising."
Glasgow have beaten the Ulstermen in just one of their last five encounters, but the New Zealander is not taking anything for granted.
"Glasgow are a formidable team, particularly at home. We have to play for the full 80 minutes against them if we are to come away with the win. We can't afford to put in a performance for 50 or 60 minutes like we have done in previous weeks."
This is the first Heineken Cup tie to be played at Scotstoun since Ulster visited the ground to play Glasgow & District back in October 1997.
ULSTER (v Glasgow Warriors): Jared Payne; Tommy Bowe, Darren Cave, Paddy Wallace, Andrew Trimble; Paddy Jackson, Ruan Pienaar; Tom Court, Rory Best, John Afoa, Johann Muller (capt), Dan Tuohy, Iain Henderson, Chris Henry, Nick Williams.
Replacements: Rob Herring, Callum Black, Adam Macklin, Lewis Stevenson, Mike McComish, Paul Marshall, Luke Marshall, Craig Gilroy.