That stay is likely to be temporary as third-placed Munster and fourth-placed Ulster face off later on Saturday but with just one game remaining, the Welsh side are on track to finish in the top two, meaning they would host a play-off semi-final.
That advantage could prove pivotal as no team has ever won an away semi-final in PRO12 play-off history but Rees is adamant his troops will buck that trend if necessary.
"If the result didn't go our way against a quality side who were top of the league, we would have the confidence to go away from home and win a semi-final," said Rees.
"We'll take it the way it comes, I don't think this result changes that. We've got to go to Connacht and they've got a lot to play for, and we've got to show the same purpose.
"They [could] be playing for a European spot next week, as well as the last game for a few stalwarts. It's a tough challenge."
Ospreys and Glasgow were locked at 3-3 heading into half-time underneath the Friday night lights at the Liberty Stadium before the hosts pulled away after the break.
Firstly, Josh Matavesi showed quick hands to set up Ben John to cross the whitewash before Webb raced free following an exquisite chip to score his side's second try.
Glasgow flanker Chris Fusaro went over for a late consolation score but that didn't stop Ospreys from ending their seven-game losing streak against the Warriors and Rees pinpointed an increased attacking intent after the interval as making the difference.
"Perhaps we kicked one or two times the first half and we allowed [Niko] Matawalu to cause some problems for us," he added.
"But we spoke about being confident and having conviction in what we're doing, and I think to go and win a league you've got to have a bit about you with ball in hand and we're trying to do that.
"We're playing with confidence but also with an understanding of where we can pressure the opposition.
"We've got great respect for them - historically the last two or three years they've had the better of us.
"But we felt there were a couple of nuances we could bring to our game, and the way we've got a confidence and a purpose to what we're doing we certainly got on top of them."
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