Candle was promoted from offensive coordinator three weeks ago when Matt Campbell took over at Iowa State.
The Rockets (10-2) positioned themselves to crack the final Top 25 for the first time since 2001, the last season they won 10 games. Temple (10-4) lost for the fourth time in seven games after starting 7-0.
Frequent driving rain hampered both offenses, but Ely went 20 for 28 for 285 yards and two scores with no turnovers.
Linebacker Ja'Wuan Woodley's jarring tackle sent the ball squirting backward 15 yards through the end zone for an early safety, and the hits kept coming from the Rockets' defense. Temple came into the game averaging 31 points but didn't reach the end zone until less than three minutes remained.
Jahad Thomas, who came into the game with 1,257 yards rushing for Temple, hurt his knee late in the first half and didn't return. He was held to 5 yards on eight carries, and his fumble led to the safety.
Toledo entered the game ranked third in the nation in red zone defense, and three times the Rockets held Temple to short field goals.
Ely and Woodley were chosen the game's most valuable players.
The Rockets were nursing a 12-9 lead in the final period when they started at their 20 following a 71-yard punt. Thompson slipped behind the secondary, caught Ely's pass in stride at his 40 and veered untouched to the end zone.
After the Rockets recovered an onside kick following Temple's touchdown, Kareem Hunt scored on a 41-yard run to seal the victory.
Toledo's Corey Jones broke five tackles to turn a short reception into a 26-yard score in the first half.
The Rockets totaled 435 yards. They moved 36 yards in the final 1:10 of the first half and kicked a 38-yard field goal on the last play for a 12-3 lead.
Temple had a great shot at the onside kick... But Toledo jumped on it with 2:45 to go. pic.twitter.com/Su7rAvhvoz— ESPN CollegeFootball (@ESPNCFB) December 23, 2015
This story will be updated shortly.