Moeen, who made his Test debut in 2014, scored 2,914 runs in 64 Tests at an average of 28.29 and claimed 195 wickets with his nagging off-spin but played little Test cricket since the 2019 Ashes series against Australia.
The selectors recalled fast bowler Tymal Mills for the first time since February, 2017.
England go into the final day at 77/0, chasing 368 to win. If they get there it will be England's highest successful Test chase ever.
Indian opener Rohit Sharma completes the top five, overtaking his captain Kohli, who has had a subdued series in England.
England reached 423/8 at stumps on the second day of the third Test. The hosts lead India by 345 runs.
England were 120/0 at stumps on the opening day after bundling out the visitors for a paltry 78.
The England pace spearhead praised India for channelising emotion well.
"There's a lot of cricket still to be played. A lot can happen within three games. It is not the time to panic," added the England captain after the stunning collapse.
Jasprit Bumrah finished with five wickets as England's second innings folded for 303.
Both sides are smarting from the mauling they received from New Zealand in June with England losing at home and India in the WTC final in Southampton.