Dyson carded a seven-under-par 63 at Kennemer Golf Club, matching the record held by himself and four other players, to record a halfway total of eight under par, one behind veteran Spaniard Jimenez.
Jimenez, already the oldest winner in European Tour history after claiming the Hong Kong Open aged 48 and 318 days last November, added a 67 to his opening 64 as he looks to claim his 20th Tour title and 13th since turning 40.
"This course suits me," said the 49-year-old, who won his second tournament in this event in 1994, albeit at a different course. "It's not a very long course but you have to have the ball in position.
"I like this kind of links course and I feel very comfortable with my game."
Dyson, whose victories at Kennemer in 2006 and 2009 both came in play-offs, carded seven birdies in a flawless round and his only dropped shots of the week so far came with a double-bogey six on his first hole of the opening round.
"I've done well in previous years and played well around it today," Dyson told Sky Sports. "I played really solid apart from the last two holes and never looked like making bogey.
"I hit a poor tee shot on the eighth, which was my 17th, and the lie determined the shot I had to play. I had quite a lot of room to pitch it on the green but had a terrible lie so had to play a little bump and run, a proper links shot, and managed to play it well.
"On the last I didn't quite strike the chip as I wanted to but it was nice to roll the putt in and have a bogey-free round."
France's Julien Quesne and England's Oliver Fisher were a shot behind Dyson as they approached the end of their second rounds, but Ryder Cup star Nicolas Colsaerts' return to action after a four-week break had already come to an end.
Colsaerts recovered from three dropped shots in the first seven holes of his opening round to get back to level par, but ran up a triple-bogey seven on the ninth, his final hole, to card a 73.
The 30-year-old Belgian had been hoping to kickstart his bid for a second Ryder Cup appearance in one of his favourite events, but withdrew before his second round with the flu.
Quesne and Fisher both birdied their penultimate hole, the par-three eighth, to card matching rounds of 65 and join Dyson in second place on eight under par.
England's Matthew Nixon also returned a 65 to finish six under alongside France's Anthony Snobeck, who added a 66 to his opening 68.
Scotland's Gary Orr, who has played just seven tournaments this season due to a recurring back injury, was another stroke behind after adding a 70 to his first round of 65.