The championship leader topped the time sheet by 0.4 seconds of his teammate Sergio Pérez, with a 1m27,901 fastest time of the weekend so far.
Verstappen topped the time sheet on his first lap lap, 20 minutes after the race, setting a 1m28.541s to degrade a Leclerc who was then leader.
It continued to improve, first at 1m28.498s before shaving another 0.15s with a sector two purple.
Despite improvements across the field, no one was able to match the Dutchman’s time, with a late challenge from Leclerc falling 0.002 seconds before Verstappen improved again.
The Monegasque driver had finished second before Pérez climbed from sixth to second, although still 0.4 seconds behind his teammate, which degraded the Ferrari man to third.
Local Mercedes favorites George Russell and Lewis Hamilton finished fourth and fifth respectively, after also showing a promising pace in Friday’s only dry training session.
Aston Martin was first on the track, with Sebastian Vettel and Lance Stroll looking forward to taking advantage of the second dry session of the weekend after Friday’s FP1 was interrupted by rain.
Fernando Alonso of Alpine was the first to get a time on the board, with a 1m34.826s, before his teammate Esteban Ocon degraded him, going 1.8s faster on his first attempt.
The McLarens of Daniel Ricciardo and Lando Norris were next to set fast times, changing first position, before Leclerc took the lead with a 1m29.452s, the first sub-1m30 time of the weekend.
Sainz was next to make a quick lap, but settled for second, reporting fights on high-speed stretches of track.
With a 10-minute session, the timing resembled a Noah’s Ark scene, with teams occupying two-on-two positions, Ferrari leading Alfa Romeo, McLaren and Alpine.
Perez was the first of the Red Bulls to mark a representative lap, splitting the Ferrari pair with a 1m29.629s, to 0.17s of Leclerc.
Russell’s first attempt was only enough for 10th place, but Hamilton took third at the start to push Sainz into fourth.
Pérez improved briefly to head the timing, but it was Leclerc who took the lead again with a 20-minute descent, with a 1m29.021s.
Verstappen took the lead, where he stayed for the rest of the session, repeatedly improving his time to seal first place before qualifying.
Russell improved to fourth place with 15 minutes to go, with a 1m28.426s, and pushed Hamilton to fifth in a race he has won eight times.
Several riders battled on turn 3, with Vettel, Perez and Sainz all running in the Village during the one-hour practice.
Sainz settled for sixth after his struggles, despite leading FP2 on Friday, with Norris in seventh.
Valtteri Bottas (Alfa Romeo), the Haas of Mick Schumacher and Alonso completed the top 10.
AlphaTauri suffered another tricky session, with Pierre Gasly and Yuki Tsunoda finishing 15th and 17th, after the Frenchman said Silverstone has exposed the weakness of his car in high-speed corners.