Before McCoy's rushing touchdowns, Pitt faced a 12-7 deficit entering the final 15 minute stanza.
His second TD came with just 52 seconds remaining.
McCoy finished with 183 yards on 33 carries and his heroics in college football's annual "Backyard Brawl" gave No. 16 Cincinnati a piece of the Big East Conference title.
Quarterback Bill Stull went 12-of-23 passing for 156 yards, one touchdown and two interceptions, both inside WVU's 10 yard line, while Nate Bynum added four receptions for 69 yards for the Panthers (8-3, 4-2).
West Virginia's Pat White went 15-of-28 for 143 yards, no touchdowns and two interceptions.
He also scored once after 12 carries for 93 yards.
Pat McAfee added three field goals for the Mountaineers (7-4, 4-2), who suffered their second straight loss in the rivalry.