It looked like Vale would become the first team to take any points off the O's this season as Louis Dodds and Jennison Myrie-Willams scored either side of two goals by David Mooney, but Kevin Lisbie made it six wins out of six for Slade's side with the decisive strike after 88 minutes.
"They never give up and that the beauty of the performance," said Slade after the 3-2 win at Brisbane Road.
"We went a goal down, then went one ahead - although that was against the run of play really - before Port Vale got themselves an equaliser.
"But we just kept plugging away and then managed, with that little bit of quality from Lis, to get the winner.
"It was a quality strike. Both him and David Mooney are capable of scoring and with the form those two are in at the minute things are going to drop to them, and if there is going to be half a chance then they are going to put it away."
Orient's opening goal brought bitter complaints from the visitors who insisted that the assistant referee had raised his flag for offside before Mooney crashed home his sixth goal of the campaign.
Slade added: "I think he put the flag up and then brought it back down. Matty Baudry was in an offside position but Moons wasn't.
"I've looked at the DVD, he was onside and he's finished off the move very well indeed. He scored again and to go in to the break 2-1 ahead was a great turnaround for us.
"We didn't deal with defending very well for either of their goals, maybe you can accept the second one a little bit because we were pushing forward, but the first one was messy and we should have dealt better with it."