Rock will take a two-shot lead into Saturday after his second-round 63, with Fowler, who carded a 66, three shots behind the Englishman.
Tyrrell Hatton, who began with four birdies in his first eight holes, finished 11 under, two shots back alongside Jens Dantorp – after the Swede bogeyed the 18th.
On another low-scoring day, 23-year-old Connor Syme shot a course record 62 – the lowest score by a Scottish player at any Scottish Open – but is back at seven under.
For the first time in his career Rock did not drop a shot in the opening two rounds after making seven birdies, as he chases a top-three finish to qualify for The Open – which begins next Thursday and is live on Sky Sports.
“My swing didn’t feel as good today but I managed to get a better score out of it which surprising but that is part of the four-round process,” Rock, 41, said.
“If you can do that when you don’t feel quite as good, that’s something and that gave me a bit of hope because I know generally, four days, I don’t get four days of everything feeling great.
“I generally have three days of feeling great and one iffy one. I hope this was the iffy one. I’m pleased that I managed to turn out a good score and had some things go my way to help me do that.”
Fellow Englishmen Lee Westwood and Eddie Pepperell also enjoyed successful days with the latter – who is also chasing a spot at The Open – producing an eagle on the par-five second hole and picking up six birdies to finish 10 under – level with Fowler.
Despite two bogeys in the opening seven holes, birdies at the 15th, 16th and 17th saw Westwood come in at four off the lead at nine-under par, alongside Scott Fernandez.
“I’m actually going to be commentating if I don’t play for BBC for a couple of days,” Pepperell said about The Open. “I’m going to be there in whichever capacity, obviously I’d rather be playing but we’ll just wait and see.
“The two similarities [between playing at the course in 2015 and this year] is that I haven’t played a practice round, and stayed in Edinburgh both times.
“That seems to be the secret for me in Gullane, just go out and have nice meals in Edinburgh and drink a bit of wine and come up here and play for four hours. Seems to be working, hopefully it works for two more days.”
Opening round leader Luke List endured a more chastening day with back-to-back bogeys on the 15th and 16th blotting his card as he ended the day at eight under.
Meanwhile, Masters champion Patrick Reed struggled too, needing three attempts to get out of the bunker at the 12th for a double bogey and could only manage bogeys on the final two holes to finish on six under.
Phil Mickelson expressed his disappointment after missing the cut and admitted he has some work to do to get himself in form for The Open.
“I would have liked to have made the cut,” he said. “I think that Gullane is such a great way to get ready for next week at Carnoustie.
“The course is firm and fast, just like Carnoustie is. I think it’s a great opportunity to get your game sharp in links-style golf.
“I had a really good first three or four months to the year. I was playing really well. I’m a little bit off, so I have a little bit of work to do.”