Fox hit just one bogey and five birdies - including on the brutal 18th which he had triple bogeyed in his first round. That birdie ended up being crucial in Fox jumping 79 places and making the cut with his final opportunity.
Fellow Kiwi Dan Hillier did not fair as well. He carded a two-over 73 to finish his tournament at nine-over and miss the cut set at three-over.
Hillier’s round was one to forget - scoring just two birdies and four bogeys but also making birdie on 18.
HARMAN IN A LEAGUE OF HIS OWN
American Brian Harman seized control of the Open with a sublime second round then watched the chasing pack huff and puff to little effect in breezy conditions at Royal Liverpool on Friday.
Early starter Harman landed a barrage of birdies on his front nine and then eagled the 18th to post a six-under 65 that left him five shots clear on 10 under.
England's Tommy Fleetwood, one of three overnight leaders after first round 66s, had raucous support but struggled to make inroads, signing for a 71 to sit on five under.
Austria's Sepp Straka emerged as a weekend contender for the Claret Jug with six birdies in a sizzling back nine for a second-round 67 to move four under.
Australian Min Woo Lee (68), compatriot Jason Day (67) and India's Shubhankar Sharma (71) were in a group on three under.
Several other players threatened an afternoon charge but the links course alongside the Dee Estuary was in miserly mood.
American Jordan Spieth, the 2017 champion, birdied three of his first six holes but struggled on the back nine and ended up going nowhere with a level-par 71 to stay on two under.
HOT PUTTER
It proved a day of hard graft for the majority with only 24 of the 156 field under par for 36 holes. But Harman, armed with a red-hot putter, made a mockery of the tough conditions.
"I've had a hot putter the last couple of days so try to ride it through the weekend," Harman, tied sixth at St Andrews last year but has not won on the PGA Tour since 2017, said.
The 36-year-old left-hander got on a roll with birdies at the second, third and fourth and then almost chipped in for an eagle on the fifth before tapping in another birdie.
Harman kept the momentum on the back nine with a sensational chip-in from off the green at the par-four 12th to avoid a bogey before icing the cake with a brilliant approach to the par-five 18th before nailing his eagle putt.
If he is looking for lucky omens, the last two winners at Hoylake -- Tiger Woods in 2006 and Rory McIlroy in 2014 -- were also on 132 after two rounds.
McIlroy arrived as pre-tournament favourite but he suffered more frustration with his putter, managing to improve only one shot from his first-round 71 to sit nine shots behind Harman and tied for 11th place.
South African amateur Christo Lamprecht came down to earth with a bump after sharing the overnight lead. Following an impressive first-round 66, he slumped to an error-strewn 79 but just made the cut for the weekend.
Argentina's Emiliano Grillo, the other first-round leader, dropped back to two under after a three-over 74.
HUGE GALLERIES
Just as on Thursday, huge galleries lined the fairways, and as well as watching the golf they saw Just Stop Oil protesters briefly halt play at the 17th with orange flares and powder.
Security staff quickly removed the individuals with the help of American Billy Horschel and there was no damage.
McIlroy gave his fans early encouragement by rolling in a birdie putt at the testing par-four opening hole and a superb rescue from a green side bunker at the fifth earned him another.
He dropped his first shot of the day at the 11th, missed a birdie at the 12th before making a superb up-and-down from a bunker at the 13th to stay below par.
A six at the 15th was cancelled by a birdie at the 18th but it was a frustrating day for the four-time major champion who will go into the weekend tied for 10th.
"Right now it's out of my hands, but at the same time, I think if I can get to minus three, four, five under going into Sunday, I'll have a really good chance," McIlroy said.
"It played really, really tough today."
Playing partner Jon Rahm, the Masters champion, made the weekend with a battling one-under 70 to sit at two over while U.S. Open champion Wyndham Clark shot a 73 to stand one-under.
Defending champion Cameron Smith eagled the 18th to squeeze inside the cut line while world number one Scottie Scheffler's birdie at 18 also spared him an early exit.
Several former Open champions will be missing at the weekend though, including Phil Mickelson, Shane Lowry, Collin Morikawa and Francesco Molinari.
Australia's Travis Smyth earned the loudest roar of the day with a hole-in-one at the 17th although at eight over and with the cut likely to be three over he will miss the weekend.
