The Ospreys went top of the Pro12 on points difference over Glasgow Warriors after Friday's 21-10 win in Swansea.
The Warriors headed into the game two points clear at the top of the table and unbeaten in their last four outings, while Ospreys were also in strong form.
There was little between the sides during a first half that was dominated by the two teams' defences. Duncan Weir put the visitors in front with a penalty goal after 15 minutes, but it remained that way for just six minutes.
Daniel Evans levelled the scores with the boot but there were no further points scored before half-time.
Ospreys made a flying start to the second period, however, to establish a lead that they would retain for the remainder of the match.
Dan Biggar's penalty put Ospreys 6-3 in front, before Ben John smashed over the line at the end of a slick passing move.
Biggar missed the conversion, but he was on target just shy of the hour after Rhys Webb gathered his own chip kick to scamper over.
By now, the rain was pouring in Swansea, allow few opportunities for either team to add to their points tally.
Chris Fusaro's converted try in the minutes that followed gave visitors Glasgow a fighting chance in the final quarter of the game, but Biggar's penalty goal nine minutes from the end established an 11-point deficit that the visitors were unable to put a dent in.
Tries: John, Webb
Pens: Evans, Biggar 2
Ospreys: 15 Dan Evans, 14 Jeff Hassler, 13 Ben John, 12 Josh Matavesi, 11 Eli Walker, 10 Dan Biggar, 9 Rhys Webb, 8 Dan Baker, 7 Justin Tipuric, 6 James King, 5 Alun Wyn Jones (c), 4 Tyler Ardron, 3 Aaron Jarvis, 2 Scott Baldwin, 1 Nicky Smith.
Replacements: 16 Sam Parry, 17 Marc Thomas, 18 Dmitri Arhip, 19 Rory Thornton, 20 Dan Lydiate, 21 Tom Habberfield, 22 Sam Davies, 23 Jonathan Spratt.
Glasgow: 15 Stuart Hogg, 14 Tommy Seymour, 13 Richie Vernon, 12 Peter Horne, 11 Niko Matawalu, 10 Duncan Weir, 9 Henry Pyrgos, 8 Josh Strauss (c), 7 Chris Fusaro, 6 Rob Harley, 5 Jonny Gray, 4 Tim Swinson, 3 Jon Welsh, 2 Pat MacArthur, 1 Ryan Grant.
Replacements: 16 Fraser Brown, 17 Gordon Reid, 18 Euan Murray, 19 Leone Nakarawa, 20 Ryan Wilson, 21 Lee Jones, 22 Fraser Lyle, 23 Peter Murchie.
Referee: George Clancy (IRFU)
Assistant Referees: Neil Hennessy, Martyn Lewis (WRU)
TMO: Derek Bevan (WRU)