The hosts lost the first test at Lord's but won the next two in Manchester and Birmingham and will go into the fourth match starting on Thursday full of confidence.
England considered playing leg-spinner Adil Rashid on a pitch that is expected to take turn but will keep faith with off-spinner Moeen Ali.
"I think the pitch will turn but our four seamers are bowling well and Mo took a massive stride in that last game," Cook told a news conference.
"If we were 3-0 up it might have been different but the series is very much alive. We stuck with Mo because he's such a valuable member of the side with the runs he has scored and in the last game he bowled really well."
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Steven Finn took two wickets in Pakistan's second innings at Edgbaston, a welcome return to form for the tall fast bowler who had been under pressure to keep his place.
Batsman James Vince was passed fit to play after dislocating a finger in the last test.
(Reporting by Ed Osmond; editing by Ken Ferris)
