NASHVILLE, Tenn. -- Fans of the Vanderbilt Commodores danced onto the field, jumping up and down as they tore down a goalpost, carried it out of the stadium and rang out sweet sounds of victory.

Then they toted the goalpost a couple of miles and tossed it into the Cumberland River.

Their school's historic win over No. 1 Alabama deserved to be celebrated this way.

Sedrick Alexander ran for two touchdowns, Randon Fontenette scored on a pick-six and Diego Pavia outplayed Heisman Trophy contender Jalen Milroe as Vanderbilt stunned Alabama 40-35 on Saturday for the Commodores' first win over a top-ranked team.

Vanderbilt (3-2, 1-1) was 0-60 all time versus AP top-five teams before Saturday, the longest such streak in the poll era (since 1936). The Commodores hadn't beaten Alabama on the field in 40 years, but they snapped a 23-game skid by making big play after big play to give coach Clark Lea his alma mater's biggest win ever.

"This is the dream, right here," Lea said. "And for the next 12 hours, I'm going to enjoy the dream. We've got more ahead of us, but this is what Vanderbilt football needs to be about: big wins on big stages. We're going to go get some more."

Alabama had just moved to the top of the AP Top 25 after an emotional win over Georgia. The Crimson Tide opened as 22.5-point favorites over Vanderbilt at ESPN BET; it was the first time an AP No. 1 team lost as at least a three-touchdown favorite since 2008, when USC fell to Oregon State as a 25-point favorite.

"We're going to find out really how much we care about each other and what it looks like moving forward," first-year Alabama coach Kalen DeBoer said. "We've been tested in different ways, really, a lot of the games here this season, and this is a different type of test now in our response."

Alexander capped the game's opening drive with a 7-yard TD to put Vandy ahead to stay. It marked the first time since 2007 that Vandy had opened a game against Alabama with a TD, the last time being Nick Saban's second game as coach.

The Tide (4-1, 1-1) helped Vanderbilt pad that lead with too many mistakes, sloppy play and penalties.

Alabama got within 30-28 with Milroe's 58-yard scoring pass to Ryan Williams.

The Commodores answered with 10 points.

Of their total, 13 points came off Milroe's two turnovers, the second a strip sack by Miles Capers recovered by Yilanan Ouattara at midfield. Pavia capped the drive with a 6-yard TD pass to Alabama native Kamrean Johnson with 5:07 left for a 40-28 lead.

Milroe tried to rally Alabama, with Williams scoring on an end around on fourth-and-1 from 2 yards out with 2:46 left.

Vanderbilt fans and players started celebrating as Pavia knelt down to run out the clock.

"Games like this change your life," Pavia said.

Milroe had his second pass of the game tipped into the air by De'Rickey Wright, who committed to Alabama and wound up at Vanderbilt. Fontenette grabbed the ball and ran 24 yards to the end zone and a 13-0 lead at 8:03 of the first quarter.

Vanderbilt jumped out to a 23-7 lead, just the second time in the past 10 seasons that a No. 1 team trailed an unranked opponent by 16 or more points.

Vanderbilt never trailed as the Commodores played keep-away, holding the ball for just over 42 minutes.

Alabama had a 312-252 yardage advantage on offense. It didn't matter, with Vandy converting 12-of-18 on third downs while wearing down the Tide's defense.

Alabama linebacker Deontae Lawson said it's early and everything remains in front of the Tide.

"We never want to feel this again," Lawson said.

The Associated Press and ESPN Research contributed to this story.