Martin, who was quickest overall in Friday's practice and therefore the last driver to qualify in the 45-car field, posted a lap at 158.297 mph for his third pole of the season and the 54th of his Sprint Cup Series career.
The 53-year-old Martin is running a limited schedule for Michael Waltrip Racing in the series this season after spending the past three years with Hendrick.
"That car was loose, but it was bad fast," Martin said. "I couldn't get it wide open from the middle off of (turn) four. It didn't look sideways, but the right-rear was out about six inches from the right-front. I couldn't get it wide open, but that was fast enough."
Martin also earned his fifth pole at Dover, four of which came when he drove for Roush Fenway Racing.
Johnson, a six-time race winner at this one-mile, concrete-surfaced racetrack, missed the pole by just 0.005 seconds.
"I hate getting beat, but Mark did an awesome job," Johnson said. "He's a great friend and a great competitor. That man can still stand on the gas."
Ryan Newman qualified third with his lap only 0.004 seconds behind Johnson.
Clint Bowyer placed fourth, followed by Matt Kenseth, the defending race winner, and Kevin Harvick.
Greg Biffle, the current points leader, qualified seventh, while Kyle Busch and his elder brother, Kurt, took the eighth and ninth positions, respectively. Denny Hamlin completed the top-10.
Other notable drivers and their qualifying positions include: Kasey Kahne (13th), Jeff Gordon (14th), Brad Keselowski (16th), Dale Earnhardt Jr. (17th), Martin Truex Jr. (18th), Carl Edwards (19th) and Tony Stewart (29th).
Josh Wise and Cole Whitt failed to qualify for Sunday's 400-mile race at Dover, which is scheduled to start just after 2 p.m. (ET).