The rookie became the first Colts quarterback since 1988 to run for rush for a pair of touchdowns in the same game, helping his team move to 3-3 for the season in the process.
For a second straight week he did not throw for a score, finishing 16 of 29 for 186 yards, but managed to get in on running plays from three and five yards out.
The Colts in total managed a season-high 148 yards rushing, Vick Ballard - starting his second game in place of the injured Donald Brown - leading the way with 84 on 20 carries.Adam Vinatieri kicked a 38-yard field goal with just over three minutes remaining to put Indianapolis four points clear - they managed to hold on in the closing stages, stopping their opponents on a crucial fourth-and-six play.
Brandon Weeden ended up being the loser in the battle of the first-year quarterbacks, though he actually outplayed rival Luck.
Weeden was 25 of 41 for 264 yards with two TDs and no interceptions, while he would have had another score had Josh Gordon not inexplicably dropped a touchdown pass in the end zone that would have given Cleveland the lead.
Trent Richardson tried to play through injured rib cartilage but managed only eight yards on eight carries in the first half. Cleveland mustered only 55 yards rushing all day.