Dillon's Chevrolet posted a top speed of 196.019 mph at Daytona International Speedway to claim front row honours for the Feb. 23 race, the first time Earnhardt's number has been used in a top-level NASCAR event since his death on the last lap of the 2001 race.
The 23-year-old rookie Dillon is the grandson of Earnhardt car owner Richard Childress and drives in the same style as the seven-times NASCAR champion.
"It's really special to have my grandson and the No. 3," Childress said. "We were fast in (pre-season) testing. You keep dreaming and thinking what would it be like to be on the pole."
Recalling the swagger of Earnhardt, rookie Dillon sported a black cowboy hat while posing for pictures with his Daytona 500 pole-winning trophy.
"It's amazing," Dillon said. "It brings momentum into the season showing that RCR (Richard Childress Racing) has speed."
Martin Truex Jr. joined Dillon on the front row for the Feb. 23 race with a lap of 195.852 mph, also in a Chevrolet. Coincidentally both cars were powered by Earnhardt Childress Racing Engines.
"It means a ton to me," Truex said. "Obviously going to a new team, this is the kind of thing that you look for."
Only the two fastest cars are locked into the front row for the 500-mile season opening race.
Although Ford drivers Greg Biffle and Carl Edwards were third and fourth fastest in Sunday's qualifying, their starting positions, as well as the remainder of the 43-car starting field, will be determined in twin qualifying races on Thursday.
Jimmie Johnson, looking to reprise his Daytona 500 victory and start his quest for a record tying seventh championship will start 14th, also in a Chevrolet.
"We are more focused on the race and really trimming the car out for single lap speed," he said. "We are kind of where we thought we would be."
Danica Patrick, last year's pole winner and the only woman driver to hold that honour, was 25th fastest.
"This car is better than our car last year," she said. "It's a bummer we weren't faster."
The 56th edition of the Daytona 500 also will see the return of three-times NASCAR Sprint Cup champion, Tony Stewart, who was injured last summer in an open wheel sprint car dirt track race.