Connacht's attempt to give coach Eric Elwood the perfect send-off never really got going and once Hogg and Maitland appeared Glasgow closed out the game.
First Hogg, fitting in at fly-half, slotted a penalty and then Maitland raced over in the corner with Hogg converting to ensure the Warriors would finish the season in third and face a trip to Leinster in the play-offs.
Connacht were presented with an early chance to take the lead but Dan Parks failed with his penalty attempt.
Instead it was Glasgow who went ahead when Ruaridh Jackson showed good invention to slot a drop goal with the help of the upright.
Glasgow extended their lead when, following good work by the forwards, centre Sean Lamont fed the ball back inside to van der Merwe who span out of the tackle and touched down and Jackson added the extras.
The visitors' flying start was slowed somewhat when prop Jon Welsh was sent to the sin-bin but it was the Warriors who should have struck again only for van der Merwe to knock-on on the line.
Connacht finally got on the scoreboard one minute before the break when Parks kicked a penalty to trail 10-3 at the break.
Jackson could have cancelled out Parks' kick straight after the interval but he couldn't put his penalty attempt between the posts.
Both sides committed errors as the game became ragged in the second half but after a strong Glasgow scrum, replacement Hogg kicked a penalty.
Hogg, who was named in the British & Irish Lions squad for the summer tour of Australia, played at fly-half after coming on with 15 minutes to go.
And it was another member of the touring party who grabbed Glasgow's second try of the game - Maitland showing great speed to cross in the corner before Hogg converted from the touchline.
A fine burst and cross-field kick from Maitland then saw Glasgow almost add a third try but despite spotting a gap Nikola Matawalu was adjudged to have knocked on in the act of scoring.
As it was there was to be no bonus-point win but it was enough to extend Glasgow's season into the play-offs.
|Connacht Rugby Score Card|
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|