Glory looked set for its first win since early February thanks to a smart headed goal by substitute Jamie Maclaren, however Mariners midfielder Nick Montgomery spectacularly hit home a deserved equaliser with two minutes of injury time remaining.
Incredibly, despite its poor run of results and modest form, Glory joins Melbourne Victory and Sydney FC on 38 points on the A-League ladder, though is kept in fourth behind those two clubs on goal difference.
"The main thing is to keep believing," said Lowe when asked what his team need to focus on.
"We are in with as good a shout as anybody. We have had a great year. We just don't want it to peter out. There is a lot more twists and turns to come in this league and we are in the mix."
Despite aiming to regain at least a temporary return to top spot, Glory looked anything but a title contender and it struggled to find fluency, with the Mariners dominating first-half possession.
"It would have been a confidence booster for all the players to go back top, but it wasn't to be," Lowe said.
"It was a fantastic goal, and just a pity to concede it right at the death.
"I thought we were a little bit off, but worked hard in the second half and it's just a shame we didn't get anything."
The Mariners deserved to go into the halftime break at least a goal to the good after attacker Nick Fitzgerald twice came close, firstly squirting a shot inches over the bar and then hitting the post after pouncing on a Dino Djulbic defensive error.
The home side comfortably had more time on the ball but Glory was not without its chances, most notably a sweet Nebojsa Marinkovic strike that was impressively tipped onto the crossbar by goalkeeper Liam Reddy.
The second half proved more even and, although Perth continued to struggle for fluency, it looked set for all three points as Maclaren perfectly glanced a near-post header past Reddy from a Marinkovic corner 12 minutes from fulltime.
For all its endeavour the struggling Mariners, and its skipper John Hutchinson - who was celebrating an A-League record 223rd appearance, seemed certain to be handed an 11th defeat of the season.
But English midfielder Montgomery ensured the spoils were shared with a sweet 25-metre strike in the second of four added minutes.
"We would have been really deflated (had we lost)," said Mariners interim coach Tony Walmsley.
"We had 60 percent possession and we hit the post. But we didn't take advantage in the second half like we wanted to."
