Leclerc beat Vettel to the front slot of the grid by a mighty 0.748 seconds as Ferrari locked out the front row.
— Formula 1 (@F1) August 31, 2019
Hamilton's hopes of participating in qualifying hung in the balance for two hours after he crashed out of final practice.
The world champion lost control of his Mercedes through the right-handed turn 12 and slammed into the barriers.
Hamilton emerged unscathed from his cockpit, but the Briton sustained extensive damage to the front of his car.
As qualifying started, Hamilton's mechanics were still working on fixing his machine when they were handed a lifeline after Robert Kubica's caught on fire following an eye-catching engine failure.
The session was suspended for 10 minutes, affording Hamilton's crew the additional time to complete their repairs. Hamilton left his garage when Kubica's Williams was removed from danger before safely booking his spot in the second phase of qualifying. Drama over.
Hamilton was in a class of one before the sport's summer break, winning eight of the 12 rounds, and establishing a commanding lead of 62 points over Mercedes team-mate Bottas.
But the resumption of his campaign has not been straightforward. On Friday, he suffered a throttle pedal failure before his uncharacteristic accident on Saturday morning. For much of the weekend, he has not been able to match Bottas either, but the Englishman found the pace required to beat the Finn and put his Mercedes in a position to threaten Ferrari.
"Final practice was terrible for me because you know how hard the guys work to build those parts and how hard they work to put the car back together," he said.
"My guys are faultless and I tried to pay them back with a good qualifying session. I am grateful I am third. I am going to give it everything tomorrow and hopefully give these guys a good race."
The Scuderia have not won this year, but their car works well at the high-speed Spa-Francorchamps track and the Italians will now be firm favourites to take the chequered flag on Sunday.
It has been 12 months since Vettel last tasted victory, dominating at this venue a year ago. But the four-time world champion will have to usurp his team-mate for a much-needed win.
Leclerc has impressed this weekend and, after an engine failure denied him victory in Bahrain, before Verstappen's fine fightback drive in Austria prevented him from winning in June, the Monegasque will be hoping it is third time lucky as he bids to open his grand prix account.
McLaren have enjoyed a resurgence this season, but the British team have not been up to scratch in Spa.
Lando Norris finished 12th, while his team-mate Carlos Sainz failed to make it out of Q1. The Spaniard qualified 17th.
The London-born Thai Alex Albon will start from the back of the field after he was penalised for a Honda engine upgrade on his Red Bull debut.