A five-under-par 66 has Casey firmly in the medal picture for Team GB in third place on 12-under while Rory McIlroy representing Ireland, is three off the pace at the Tokyo Games after he shot 67.
Both are joined in the top 10 by their respective countrymen Tommy Fleetwood and Shane Lowry, who are tied on nine-under.
Casey had to finish his second round first in the Japanese capital and then attempted to reel in American Schauffele, who finished with a three-under-par round of 68 to extend his score to 14-under.
Former world number three Casey hit four birdies on the front nine and recovered from a bogey at the 14th to finish strongly with back-to-back birdies.
Japan’s Hideki Matsuyama is second on 13-under while McIlroy is in a tie for fifth after four birdies on the back nine kept him in contention for a medal.
Team GB’s Fleetwood was the big mover of the third round with a seven-under 64 which could have been better were it not for consecutive bogies at four and five.
A birdie at the 18th – to make it five overall on the back nine – lifted the Englishman to joint-ninth on 10-under alongside Ireland’s Lowry.
Lowry was one of many to bogey the 14th but is only four shots off leader Schauffele ahead of a potentially thrilling final day at Kasumigaseki Country Club.