Ulster proved to be too strong for Celtic League rivals Glasgow Warriors and left Scotstoun Stadium as 8-19 winners in Heineken Cup pool 4.
Ulster, who had crushed Castres 41-17 in their opening Pool 4 match in Belfast last weekend, had led 6-3 at half-time thanks to two penalties from Paddy Jackson.
Back row forward Chris Henry extended their lead with their only try of the game after 68 minutes with Jackson adding the extras for 13-6.
Jackson added two more penalties to give 1999 champions Ulster a cushion which made Glasgow's last minute try from Fijian replacement scrum-half Nikola Matawalu a mere consolation.
"It's not easy to come here and get a victory as other teams I'm sure will find out," said Ulster head coach Mark Anscombe.
"We showed a lot of character, the boys battled their way through tough conditions against a very good team. "
"You have got to be able to work through things because the game of rugby doesn't always go the way you want it."
Final Score Glasgow 8 (3) Ulster 19 (6)
Tries : Matawalu
Penalties: Jackson 4
Referee: Mathieu Raynal (Fra),
Assistant ref: Christophe Berdos,
Assistant ref: Jean-Luc Rebollai
TMO: Vincent Azoulay
Citing Commissioner: Yann Le Dore.
Glasgow Warriors: Stuart Hogg; Byron McGuigan, Peter Murchie, Peter Horne, Alex Dunbar; Ruaridh Jackson, Henry Pyrgos; Ryan Grant, Dougie Hall, Michael Cusack, Tom Ryder, Alastair Kellock(c), Josh Strauss, Chris Fusaro, Ryan Wilson
Replacements: Finlay Gillies, Ofa Fainga'anuku, Gordon Reid, Tim Swinson, Rob Harley, John Barclay, Scott Wight, Nikola Matawalu.
Ulster Rugby: Jared Payne; Tommy Bowe, Darren Cave, Paddy Wallace, Andrew Trimble; Paddy Jackson, Ruan Pienaar; Tom Court, Rory Best, John Afoa, Johann Muller(c), Dan Tuohy, Iain Henderson, Chris Henry, Nick Williams Nanai.
Replacements: Rob Herring, Callum Black, Adam Macklin, Lewis Stevenson, Mike McComish, Paul Marshall, Luke Marshall, Craig Gilroy.