But they arrived on 10 under par by very different routes.
Stenson bogeyed his last two holes for a 70 – six worse than his first-day score – while Coetzee birdied two of his last three for a second successive 67.
“It’s never fun to finish with two bogeys, but you gain some, you lose some – sometimes that’s the way it is,” said Stenson.
The former world No 4, down at 124th after more than two years without a win, had been three clear of the field when he followed a chip-in eagle on the long sixth with a tap-in birdie at the 441-yard next. “I’m in a good position and I’m feeling very good. I had to fight a little bit early on, but I managed to stay patient.”
Coetzee has yet to taste victory on the European Tour and has yet to play in a major championship but that will change in three weeks’ time – he earned a place in the Open at the sixth hole of a play-off earlier this month.
The 24-year-old from Pretoria is a four-time winner on his home circuit and stated: “I believe I can win every single event there and the more I get in contention in Europe the more I will believe I should be up there.”
One shot back in third place is Spain’s Pablo Larrazabal – the player Coetzee beat in near-darkness at the Open qualifier.
He could still make it to Sandwich with a top-two finish this weekend, however, and commented: “I really want to play, so I am just going to go for it.”
Larrazabal is also looking to make amends for what happened at this tournament a year ago.
He led with three holes to play, but double-bogeyed the 16th, bogeyed the 17th and lost by two to England’s David Horsey.
On his return to the 16th yesterday he spun his approach into the cup for an eagle two.
“It’s given me confidence – I’m not scared of that hole,” he said.
Sergio Garcia, not in the Open yet either, is six strokes back after a 71, but world No 3 and local hero Martin Kaymer moved to six under with a 68.
The cut fell at two under, so Colin Montgomerie made it with nothing to spare the day after his 48th birthday.
Malton’s Simon Dyson missed the cut after following his opening round 74 with a 70 but the other three Yorkshire players involved will be in action this weekend.
Hull’s Richard Finch moved up the field into a share of 15th place with rounds of 70 68, Sheffield’s Danny Willett dropped back after following his 66 with a 74 and Harrogate’s John Parry recorded a second successive 71.