Hillier was overtaken by Dutchman Joost Luiten, who shot a seven-under 65 to lead by three shots from compatriot Daan Huizing at Golfclub München Eichenried.
After carding 71, Hillier is in a three-way tie for third with Italy’s Edoardo Molinari and South Africa’s Thriston Lawrence.
Hillier holed a 14-foot putt to birdie the second hole and had another two birdies on the front nine, and missed a good chance as he failed to get up and down after driving right up to the fifth green.
But he dropped a shot when he bogeyed the 11th and then suffered a double-bogey when he three-putted on the par-4 13th.
He recovered to birdie the 14th and then played to par on the final five holes.
Luiten, 37, is now closing in on his seventh DP World Tour European title after seven birdies in a bogey-free round.
“Today was pretty much flawless,” he told the DP World Tour website. “I didn’t really get into trouble that much and if I did miss the fairway I hit a great shot and still created a birdie chance. I made some nice birdies coming down the last four or five holes and it was nice.
“It would mean a lot to me to win but that’s not just me, that’s everybody. We’ve got another 18 holes here [on Monday NZ time] and I need to keep my head cool, hit some shots like I did today and we’ll see what happens. I’ll try to play shot by shot like I did today.”
Following up an opening 69, he birdied the fourth and while he gave the shot back on the sixth, a hat-trick of gains saw him turn in 33 and share the lead.
Further birdies at the 11th and 15th moved him ahead and he kept the lead as he bounced back from a bogey on the 16th with a gain on the last, before later being overtaken by Hillier.
Luiten holed a six iron from 203 yards on the eighth for his perfect shot to go with six birdies and two bogeys.
Home favourites Marc Hammer and Marcel Schneider, Frenchman Adrien Saddier, South African Jayden Schaper and Finn Sami Välimäki were three shots off the lead.
Daniel Hillier of New Zealand looks pensive as lines up his putt on the 12th hole during day three of the BMW International golf tournament in Munich.