Christian, who rushed for 82 yards on 19 carries, gave TCU (3-0) the lead for good on a 1-yard scoring run with six minutes left in the third.
Stanford (1-2) appeared to tie the game early in the fourth on Doug Baldwin's 49-yard punt return for a touchdown. Officials reviewed the play and determined Baldwin stepped out of bounds at the TCU 13.
Three plays later, Coleman intercepted Tavita Pritchard's pass in the end zone to thwart Stanford's comeback attempt.
The Horned Frogs have won 46 of their last 52 home games and 11 of 13 overall against schools from BCS conferences.
Kickoff was moved up to noon because of the hurricane that hit the Texas coast early Saturday.
Despite the earlier start time, it began raining harder in the second half and winds from the outer edge of the storm gusted to more than 30 mph in the fourth quarter.
Richard Sherman returned a blocked punt 21 yards for a touchdown as Stanford rallied from a two-touchdown deficit to tie the game at 14 before halftime.
The Horned Frogs took the lead on their second possession in the second half. Their nine-play, 51-yard drive was capped by Christian's short run.
TCU's defense made another key stop midway through the fourth.
On fourth-and-1 from near midfield, linebacker Robert Henson stopped Toby Gerhart for no gain.
The Horned Frogs cashed in on Henson's play as they drove down to the 1 and took a 24-14 lead on Ross Evan's 23-yard field goal with 2:24 left.
TCU quarterback Andy Dalton, who capped the scoring with a 10-yard run, passed for 145 yards and rushed for 91 more.
Gerhart rushed for 45 yards and caught three passes for 42 yards, and Pritchard was 11-of-21 for 122 yards.
The Horned Frogs jumped out to a 14-0 lead on touchdown runs from Justin Watts and Jeremy Kerley.
The Cardinal had only 44 yards of offense on its first four drives before driving 78 yards on five plays to get on the scoreboard.
On a receiver end around, Baldwin ran 38 yards for a touchdown. Baldwin made several tacklers miss, including a nice move on Rafael Priest at around the 15 that sprung him toward the end zone.
Stanford tied the score when Mark Mueller blocked Anson Kelton's punt. Sherman picked up the loose ball and jumped over a would-be tackler to tie the score at 14 with 6:18 left in the first half.