In a matchup of the two teams at the bottom of the Pac-12 South, the Utes raced to a 21-0 first-half lead before the Buffs roared back.
But the Buffs forced a Utah punt that was downed at the 10 -- Tom Hackett's third kick inside the 10-yard-line.
On the next play, defensive end Reilly dropped back from the line and caught the ball at the 21-yard-line. A year of frustration was evident as Reilly threw the ball high into the south end zone stands before he was greeted by a horde of celebrating teammates on the sidelines.
Adam Schulz, a former walk-on who was pressed into service when starter Travis Wilson was sidelined with an intracranial artery injury three weeks ago, completed 19 of 33 passes for 233 yards for Utah.
Utah broke a five-game losing skid and Dres Anderson became the seventh Ute to reach 1,000 receiving yards in a season, the first since David Reed had 1,188 in 2009. He caught seven passes for 94 yards against the Buffs, which put him at 1,002 for the season.
Liufau was pressured mercilessly in the first half but finished 23 of 46 for 241 yards and two touchdowns for the Buffs.
In the third quarter, Liufau finally had time to throw and lofted a pass to Scott Fernandez down the middle of the field for a 34-yard touchdown.
Just when it looked like the Utes would put the game out of reach late in the third quarter, the Buffaloes made a big play. Jake Murphy caught a pass near the goal line and as he reached for the end zone, he lost the ball and Jeffrey Hall returned the fumble for 42 yards. A 15-yard face mask penalty on Schulz tacked on 15 yards.
The ensuing drive stalled at the Utah 2, but Will Oliver kicked a 19-yard field goal to draw Colorado within 21-10 with 12:17 to play.
Andy Phillips countered with a 46-yard field goal for Utah before the Buffs made their late push.
The opportunistic Utes used two fumble recoveries to spark short touchdown drives in the first quarter. The Buffaloes had just 11 fumbles all season but Liufau was sacked by Tenny Palepoi and lost the ball at the Colorado 34.
Schulz completed three passes on the drive to Jake Murphy, the last of which was a 16-yard touchdown. Murphy, in his third game back from a broken wrist, had eight catches for 93 yards.
Later in the first quarter, Liufau was hit just before he threw by Hunter Dimick and LT Tuipolutu took the ball off a bounce and rumbled to the Colorado 6-yard-line. On the next play, York ran up the middle and Utah led 14-0.
York scored again from one yard out after Dres Anderson highlighted an 80-yard drive with a 49-yard dazzling catch. In his final game as a Ute, York posted a career-highs in yards and carries (31).
In the first half, Addison Gillam intercepted Schulz and returned it to the Utah 5. But the Buffs couldn't punch it in and Reilly, who had 14 tackles, stuffed Tony Jones for a 4-yard loss on fourth-and-goal.
Both teams have struggled since joining the Pac-12 in 2011 and this season-ending contest have been tight all three years with Utah claiming the last two.
The Utes, who beat Stanford and lost nail-biters to Arizona State and Oregon State, have wondered all year what could have been without the key injuries and few friendly bounces of the ball.
After a 10 consecutive season ending in bowl games, the Utes have now finished back-to-back campaigns with losing records.
Ohio State remained No. 1 in the AP Top 25 and tied a poll record Sunday despite lagging support from voters. Meanwhile, No. 2 TCU and No. 3 Baylor edged forward and No. 4 Michigan State slipped.
Texas cornerback Kris Boyd has apologized for retweeting a Texas A&M fan during halftime of Texas' 50-7 loss to TCU on Saturday.
The Big 12 on Sunday acknowledged an officiating mistake that incorrectly awarded Oklahoma State a first down Saturday and said the officials involved would be disciplined.
Georgia coach Mark Richt says he's sticking with Greyson Lambert, who was just 10-for-24 for 86 yards in a loss to Alabama, as the Bulldogs starting quarterback.
Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.