Fly-half Dan Biggar grabbed an early try for the Ospreys, adding to a penalty try, and there were second half touchdowns from Tom Smith, Ashley Beck and Jerry Collins.
The defending champions were without a total of 17 players due to international commitments or injuries. Glasgow Warriors were also minus a clutch of Scotland players and hampered by injuries but were able to name the same side that drew with the Dragons last weekend.
This was repeat of last season's Magners League semi-final and the Warriors' first trip back to Swansea since that 20-5 defeat.
But right from the start, when Duncan Weir put his kick-off straight into touch, the Ospreys more than edged the opening quarter.
It was a dominance that was based on a big scrum and some lively players behind it such as man-of-the-match Rhys Webb and the centres Ashley Beck and Sonny Parker.
And the Ospreys scrum did the damage which led to a ninth minute penalty try after Glasgow had infringed at three consecutive five-metre scrums.
A Biggar drop goal stretched the home lead to 10-0 before the young number 10 sidestepped his way past Ed Kalman and over the try-line after an incisive break by scrum half Webb.
But just as the Ospreys looked as if they were going to run away with the victory, the Warriors came back with two Weir penalties in as many minutes - the second from the 45-metre range.
The Scottish outfit should have had two tries before the interval - winger DTH van der Merwe and centre Peter Murchie both got over the line but failed to ground the ball.
First, Beck turned van der Merwe, who should have been released earlier by Peter Horne, and then Hanno Dirksen prevented Murchie from dotting down. A pass from Murchie to the supporting Stuart Hogg looked the better option.
17-6 in front at the break, tt took the Ospreys just five second half minutes to extend their lead. The home side went through the phases before Webb put flanker Smith over for the score.
And six minutes later, Biggar slotted over his first penalty to complete his full house of points and take the Ospreys' lead out to 21 points. Glasgow, who were winless in their previous five league matches, struggled to respond.
The Ospreys were given a further lift when their British & Irish Lions prop Adam Jones came on for the final 22 minutes in his first appearance since injuring his elbow two months ago.
The Ospreys finished with a flourish, bringing up the bonus point with a length-of-the-field try started by replacement winger Tom Isaacs and finished off by Beck.
A drive from a lineout saw replacement back rower Collins go over for the fifth try, three minutes from time, to put the icing on the cake.
Speaking after the game, Ospreys head coach Sean Holley said: "There were elements of the performance we weren't happy with. At half-time we were annoyed that we'd perhaps lost our shape a little bit, perhaps tried to win it from our own half. That was probably a result of youthful exuberance and scoring too early.
"In the end, we've knuckled down and got the win we wanted. It rounds off a good block of games for us, so we'll take that. This win equals an Ospreys record (of seven in-a-row), which is great.
"It's just a shame that we've got three weeks off now, we just want to play. The form of the team has been excellent, they've been extremely diligent and hard working, and they've stepped up to the plate when they needed to."
"We've said to this group that if we didn't do well at this period then there wouldn't be much to play for at the end, and now, we're in a strong position."
Giving his assessment, Glasgow boss Sean Lineen said: "The team is a bit low in confidence at the moment and we're a bit low on leadership. Losing 16 players (to international duty and injuries) is just too much for us and that's the honest truth.
"We butchered two tries in the first half. We played quite well during that period but just couldn't score.
"Our night was summed up when the Ospreys scored their fourth try. We were camped on their line and some guy tried to be the hero and go himself just for them to score at the other end. It's tough, really tough.
"I've said it before, these guys are learning the hard way and we've just got to dig deep and get through this patch."
|Ospreys Score Card|
|Glasgow Warriors Score Card|