Duke (3-1) struck for 21 points during a six-minute span of the third quarter, taking the lead on the way to eclipsing its 2020 win total.
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Holmberg's scoring runs came from 4, 1, 3 and 13 yards. He threw for 328 yards, completing 22 of 29 passes.
Holmberg became the eighth Duke player with four rushing touchdowns in a game and the first since quarterback Brandon Connette ran for four in 2013.
"It's part of the game plan," Holmberg said of his 17 carries for 88 yards. "The O-line did their part. The receivers (blocked well) on the perimeter."
Holmberg needed brief medical attention following his final TD run. He said he just had the wind knocked out of him.
Duke's Mataeo Durant ran for 124 yards on 21 carries, including a 57-yard touchdown for the game's first points. Jake Bobo made seven catches for 105 yards.
"We've got a lot of weapons and we've got to continue to grow and get better," Duke coach David Cutcliffe said. "I think our offense is playing at an extremely high level."
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Kansas quarterback Jason Bean went 19-for-32 for 323 yards with two touchdowns and two interceptions. Trevor Wilson had 122 receiving yards on five catches and Devin Neal ran for 107 yards and a touchdown on 17 attempts.
Kansas (1-3) led 24-21 at halftime courtesy of Neal's 1-yard run on fourth down with 1:04 left. The Jayhawks boosted the margin on Jacob Borcila's 29-yard field goal on the first possession of the second half.
"You go out every drive knowing you've got to respond," Holmberg said.
Duke posted the next 24 points, aided by linebacker Shaka Heyward's interception of Bean, setting up Holmberg's 3-yard run two plays later.
"They run a lot of explosive plays," Kansas coach Lance Leipold said. "We didn't tackle as well as we need. That continues to be a spot we need to work on."
Kansas had three possessions inside the Duke 25 in the first quarter. The second time, Borcila booted a 50-yard field goal for the Jayhawks' first points. Bean's swing pass to Torry Locklin resulted in a 20-yard touchdown.
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The Blue Devils have won three games in a row for the first time since September 2019. Since then, six of the team's seven victories have come in home games.
The Blue Devils open Atlantic Coast Conference play next week at rival North Carolina.
"Going into ACC play, there's no room for error," defensive end Ben Frye said. "We've got to bring it right away. ... So many things to clean up. So many things to look at."
Cutcliffe said the Blue Devils need to click it into gear quicker.
"Certainly love playing better in the second half because we didn't get off to a great start," Cutcliffe said.