Seven-time world champion Hamilton was the quickest man in the desert on Friday, but he ended the final action before qualifying 0.263 seconds behind Red Bull's Verstappen.
Hamilton wrapped up his sixth title in seven seasons at the Turkish Grand Prix a fortnight ago and vowed to end the season by continuing his dominant streak which has seen him win 10 of the 14 races staged in 2020.
Verstappen has been the only driver able to keep up with the all-conquering Mercedes team, and the Dutchman will hope his pace here will enable him to contend for pole later on Saturday.
Albon is competing in a new chassis after writing off his last machine following his hefty impact with the barriers at the final corner in practice on Friday.
The London-born Thai, fighting for his future in the sport with Racing Point's Sergio Perez in the frame to replace him at Red Bull next season, will take some confidence from finishing in the top four, albeit almost seven tenths down on his team-mate.