After the visitors resumed on four for no loss, Pakistan skipper Misbah-ul-Haq introduced left-arm spinner Zulfiqar Babar in the eighth over but it was part-time spinner Shoaib Malik who earned them the breakthrough in his first over.
Moeen went for a cross-batted slog that resulted in a top edge and slip fielder Younus Khan had all the time in the world to step back and position himself under the skier.
Bell asserted himself early, stepping out to hit Babar for a six over long-off, while Cook often employed the sweep shot to thwart the spinners.
Cook looked set for his 46th test fifty but was denied by Shah, who had dismissed the England captain in both innings of the previous test.
Cook tried to glance the delivery from the leg-spinner but only managed to deflect it onto his pads before Azhar Ali took the catch at forward short leg.
Joe Root (four) soon joined his captain back in the pavilion after Sarfraz Ahmed took a low, one-handed catch off Rahat Ali to send him back.
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
