Peyton Hillis also scored three TDs, the last in the third overtime. Felix Jones ran for the critical 2-point conversion to make it 50-42 for the Razorbacks (8-4, 4-4 Southeastern Conference).
LSU (10-2, 6-2) responded when Matt Flynn found Brandon LaFell for a 9-yard TD, but Matterral Richardson intercepted the 2-point conversion attempt, and Arkansas' bench emptied onto the field in triumph, having ending the nation's longest home winning streak at 19 games.
"Hey, we were the best team in the country today," boasted Houston Nutt, who is rumored to be on his way out as the Razorbacks' head coach. "To come down here in Baton Rouge and win is huge."
McFadden, last year's Heisman Trophy runner-up, rushed for 206 yards 32 carries and now has 1,725 yards rushing this season, breaking the single-season record of 1,647 he set last year.
No doubt there are West Virginia and Ohio State fans who'd vote for McFadden for Heisman if they could.
By knocking off LSU, which was in first place in the BCS standings, Arkansas boosted the national championship hopes of the Mountaineers and Buckeyes.
"Certainly, he had a Heisman performance today," LSU coach Les Miles said. "Right now, there's a goal of our football team taken off the board and it's sad. ... Tonight, we'll be sick."
McFadden often took direct snaps in "Wild Hog" formation. He was a triple threat to run, hand off or throw, and looked quite comfortable in the quarterback role. He executed a flawless play-action fake on his 24-yard touchdown pass to Hillis in the fourth quarter.
He was most dangerous running the ball, as usual. His second TD, again coming after he took the direct snap, went for 73 yards.
Miles said he thought he had a good plan for the "Wild Hog" formation, with two defenders shadowing McFadden. LSU linebacker Ali Highsmith did his best, making 15 tackles.
"There's a point where I thought we were going to defend that thing pretty well," Miles said. "There were two pretty good LSU tacklers ready to tackle that guy and he didn't go down. It definitely affected us."
McFadden wasn't the only running back LSU had trouble wrapping up.
Hillis and Jones each ran for 89 yards as Arkansas finished with a 385 yards on the ground against one of the best run defenses in the country.
It's the second time this season the Tigers have fallen while at No. 1 and it's probably too late in the season now for them to get another chance.
The winner of tomorrow night's game between No. 2 Kansas and No. 3 Missouri will likely take over the top spot in the rankings and the BCS standings. No. 4 West Virginia, which was third in the BCS standings, has a chance to sneak up to at least No. 2 in each with a win over Connecticut.
As for Ohio State, the Buckeyes are done and waiting it out. They were fifth in the last BCS standings.
Whichever team reaches No. 1, it'll be the fourth top-ranked team in this season of instability. The last season that had four No. 1s was 1997.