A late downpour meant the field launched for the Saturday race behind the safety car ahead of a rolling start.
Drivers reported improved conditions to immediately ditch full wet tyres for intermediates, but 10 drivers stayed out to avoid losing time in a busy pitlane.
Piastri pitted straight away for intermediates, while Red Bull took the "safer call" by delaying Verstappen's stop for another lap - even if he was eventually held in the pit box for a longer 3.2 seconds to avoid clipping Lando Norris.
This handed Piastri a lead of 1.7s ahead of the safety car returning when Fernando Alonso crashed out. But Piastri only survived in the lead until lap six, with Verstappen catching a tow through Eau Rouge to pass down the Kemmel Straight.
Piastri reckoned he was "no match" for the chasing RB19. The Australian said: "We tried our best. We boxed when the safety car came in. We led a few laps. But we were no match for Max."
Piastri reckoned the Alonso-induced safety car might have worked to his advantage as it reduced the amount of time he would have to defend from reigning double champion Verstappen.
However, he then summitted Eau Rouge and realised Verstappen was "basically on top of me already".
Piastri continued: "I thought the safety car was going to be in my favour, as it meant less [sic] laps to try and hold him behind.
"But I looked out of Turn 1 [La Source] and I feel like I got a decent restart. I looked at the top of Eau Rouge and he was basically on top of me already. I couldn't keep him behind on the straight."
Piastri also heaped praise on the continued resurgence of his McLaren team, which scored podiums in the most recent British and Hungarian GPs thanks to Norris.
The first-time F1 podium finisher said: "Clearly, we have a little bit more work to do. But I'm very happy to get the good points…
"I think apart from Max, our pace was really strong. So, full credit to the team again.
"The last three weekends we've had, it's been pretty special compared to where we have been, so I can't thank them enough for the car. "We've still got a little bit of work to do clearly to get right to the top.
"But it's a lot nicer to be up there and to lead my first laps was a day I won't forget."
