That topped the mark of 4.43 seconds set by Emanuel Lawson in 2006.
He was faster than all but two of 23 running backs who ran the 40 at the NFL scouting combine this week, and he was 0.12 seconds faster than Jadeveon Clowney's time at the 2014 combine.
Sweat had 11 1/2 sacks and 14 tackles for loss last season after posting 10 1/2 sacks and 15 1/2 tackles for loss in 2017.
He said Saturday that he models his game after "old-time pass rushers like Jason Taylor," and when asked what would set him apart among this year's deep D-line class, Sweat said, "I think I would separate myself with my effort and my play. Just getting after the QB is what I do best."
Also Sunday, Alabama D-lineman Quinnen Williams ran a 4.83 40-yard dash. That's the fourth-fastest combine time by a 300-plus pound D-lineman since 2003.
His Tigers teammate, defensive tackle Dexter Lawrence, sustained a minor thigh injury while running his 40 and didn't participate in the other drills. He is expected to work out at the Tigers' pro day later this month.