© PA Photos
Paddy Jackson kicked 14 of his side's points in a scrappy affair at the Scotstoun Stadium.
The match got off to a very slow start with Rob Horne and Paddy Jackson penalties making up all the first-half points as Ulster went into the break 6-3 up.
After an hour of play, Chris Henry found the opening try from a catch and drive lineout after intervention from the television match official.
Jackson extended Ulster's lead with three more successful penalties before Niko Matawalu gathered a cross-field kick to earn a consolation try for Glasgow.