The overnight joint-leader extended his lead further with another gain at the 17th as he covered the back-nine in 31, and he picked up another shot at the fourth before making his only mistake of the day three holes later.
McIlroy's Ryder Cup team-mates Westwood and Poulter both struggled for consistency, with Poulter scrambling four pars and a birdie over the first four holes before finding water with his tee shot to the fifth after being distracted by mobile phone sounds in the crowd. and running up a double-bogey.
Hatton was one of only three players in the top 24 to fail to break par on a day of low scoring at Close House in northern England.
Westwood is one of a trio of Englishmen on four under after rounds of 66, along with fellow Ryder Cup stars Ian Poulter and Matt Fitzpatrick.
That round will include Rory McIlroy after the world No. 6 responded to two bogeys in his first five holes that left him hovering around the projected cut.
Four-time major victor McIlroy managed to fight back from bogeys at his second and fifth holes to birdie his sixth, 11th and 17th holes and finish two shots inside the two-under par cut-off mark.
"So he's a legend of the game and if this is it, then everyone should just applaud what a great career he's had". Jack has a better record [winning 18 majors, four more than Woods], but I don't know if he played better golf.
McIlroy only confirmed his participation at this week's tournament at Close House after missing out on qualifying for the end of season Tour Championship, capping a hard 12 months for the six-time major victor, during which he has struggled with his fitness and split from his long-time caddie JP Fitzgerald. "I'm not really looking ahead at anything".
"I spent a bit of time with him over the past few months and he's waiting on his doctors to tell him when he can do things again".
Swede David Lingmerth was also in the clubhouse at 10-under after a 62. "Katie's not here but I sent a big bunch of roses".
"Obviously I'm here to try and win and I'm here to try and play well, but if it doesn't happen I'm okay with that", the world number six added.
"I am happy with the score and despite a couple of niggles while I was playing that weren't that good, had the opportunities when they came, and we were able to post a pretty good number", Coetzee said.