The incident robbed Red Bull the chance of a one-two finish, with Daniel Ricciardo's sublime charge through the field showing just how much pace the team had in pace over its rivals in the closing stages.
Both Red Bull drivers were serviced for fresh Soft tyres when the Safety Car was called on lap 31 of 56, and once the track was cleared Verstappen and Daniel Ricciardo made their charge towards the front.
The Australian, whose Bahrain GP lasted less than two laps after an electrical shutdown, posted a lap just good enough to squeeze through to the next phase.
Sergey Sirotkin wasn't so lucky, the Williams driver missing out by an agonising 0.049s.
Warmer temperatures are predicted for Sunday and Mercedes, who struggled to get the tyres in the right temperature window, hoped that could help them in the race. Hamilton has now gone six races without a race win - his longest such streak since 2013. There was no coming back for the Ferrari from there and the driver finished in the eighth place.
This time, the Mercedes duo found more performance with Hamilton and Bottas going first and second.
Verstappen had changed onto fresh soft tyres before attempting to overtake Vettel's Ferrari for third place at the hairpin on lap 43 but locked up, ramming into the German's auto. Carlos Sainz took ninth in the second Renault, 0.287s off his teammate Hulkenberg, with Romain Grosjean tenth in the Haas.
Force India's Esteban Ocon, McLaren's Fernando Alonso and Stoffel Vandoorne, who tried and failed to successfully make a tow work for each other, and Toro Rosso's Brendon Hartley were the others to miss out on the pole position shootout.
On lap 43 he saw an opportunity to overtake at the Turn 14 hairpin.
Sebastian Vettel set a blistering new lap record for Ferrari as he stormed to pole position for Sunday's Chinese Formula One Grand Prix ahead of champions Mercedes. Ricciardo's win means Red Bull and Ferrari have both claimed a win before Mercedes in 2018 and Hamilton knows he will need to improve to stay in championship contention.
Bottas was asked if he was surprised by the Ferrari advantage.