Robinson, who caught eight passes for 83 yards, beat safety Idrees Bashir on the winning play to offset a 43-yard field goal by the Tigers' Ryan White earlier in the third overtime.
Memphis (4-4, 2-3 Conference USA) sent the game to triple overtime when Scott Scherer completed a 4-yard scoring pass to Billy Kendall on fourth down.
Houston (3-4, 2-1) forced the overtime with a nine-play, 84-yard drive in the fourth quarter. McKinley connected with tight end Stephen Cucci four times for 26 yards on the drive, including a 5-yard touchdown with 3:46 to play.
Memphis, which generated little offense in the game, held a 17-10 lead early in the fourth quarter when the Tigers capitalized on a Houston fumble at its own 25. Two plays later, Scherer hit White with a 25-yard touchdown pass.
Memphis led 10-7 at the half, capitalizing on other Houston miscues in the second quarter.
Through the first quarter, there was little offense on either team's part as most of the action involved exchanging of punts.
The Tigers first break came when Michael Stone intercepted McKinley's pass and returned it 28 yards to the Cougars' 5. Two plays later, Sugar Sanders scored from 2 yards out.
Houston answered with the longest drive of the half, marching 80 yards in 13 plays, the final 7 yards coming on a pass from McKinley to Tommie Baldwin. During the drive, McKinley connected with Robinson four times for 40 yards.
A muffed snap by Houston punter Mike Clark gave Memphis the ball at the Cougars' 12, leading to White's 38-yard field goal as time ran out in the half.