Red Bull's double defending world champion rode his luck when McLaren's Piastri snatched the lead by making an early pit-stop to switch from wet to intermediate tyres, to storm back and win by 6.6 seconds.
Verstappen's win extended Red Bull's record this year to 14 wins from 14 races -- 11 grands prix and three sprints.
He said he agreed with Red Bull's strategy decision, which cost him the early lead, but ensured he was able to go on and win.
"I think it was just a safer call," he said. "I could come in first, but then I might be blocked by other cars. There might be a Safety Car and then you lose out massively, so I didn't mind to stay out.
"I mean we lost one position, but we know we are quick and you could see that when we put the 'inter' tyres on we were flying so it was ok."
Looking ahead to Sunday's Grand Prix, when he will start sixth after taking a five-place penalty, Verstappen said his chief concern was not only the possible change of conditions, but also the risk of a collision at La Source, the hairpin first corner.
"I need to pass a few cars so I think the biggest risk is just lap one, especially Turn One. It's always very tricky there so, as long as we stay out of trouble, I think we will have a quick car."
Ferrari's Charles Leclerc will start Sunday's main event from pole.
Piastri came home a strong second ahead of Pierre Gasly, who gave the beleaguered Alpine team something to celebrate, with Carlos Sainz and his Ferrari team-mate Charles Leclerc finishing fourth and fifth.
Seven-time world champion Lewis Hamilton came home fourth on track for Mercedes, but was demoted to seventh behind Lando Norris, in the second McLaren, after taking a five-second penalty for a clash with Red Bull's Sergio Perez.
George Russell was eighth in the second Mercedes ahead of Esteban Ocon in the second Alpine and Daniel Ricciardo, enjoying his second weekend with Alpha Tauri.
"I am very happy," said Piastri. "We tried out best and led for a few laps, but we were no match for Max. But it's nice to be up there in P2. All credit to the team."
The race began 35 minutes late, after delays caused by heavy rain, with all 20 cars on full-wet tyres for the start behind the safety car.
The race distance was reduced to 12 laps, but it was obvious that in the improving conditions all 20 cars would dive into the pits for intermediates as the race was reduced to 11 laps.
Finally, the safety car came in and Verstappen accelerated into Pouhon while Piastri, Sainz, Perez, Gasly and Hamilton all dived in immediately for intermediates leaving Verstappen leading Leclerc at the front.
"We need to box this lap," said Verstappen, who then pitted, emerging second behind Piastri with Gasly, Perez and Hamilton behind him, all three gaining from their instant pit-stop decisions.
By lap three, the Australian was eight-tenths ahead, his wet-set-up car resisting the Red Bull, which had superior straight-line speed, before Fernando Alonso spun out at the exit of Pouhon.
He was unhurt, but he had his first non-finish of the season to mark his 42nd birthday.
The safety car was deployed while Red Bull told Verstappen Piastri's left-hand tyres were "suffering".
"I'm not surprised, he's drifting everywhere," said the Dutchman who picked his moment after the re-start, with five laps to go, to blast past Piastri down Kemmel Straight.
Gasly stayed third as Perez and Hamilton tangled when the Briton dived down the inside at Stavelot, but he succeeded later in the lap at La Source and both Ferraris followed in overtaking the Mexican.
His team-mate made short work of establishing himself as leader and was four seconds clear of Piastri by lap nine as Hamilton, fourth, was given a five-second penalty for his earlier contact with Perez.
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