Harman pulled clear of the field with a stunning six-under-par round of 65 on Friday to move to 10 under as windy conditions and the 82 bunkers at the Royal Liverpool course made it a difficult day for low scoring.
But the 36-year-old's temperament is set to be tested over the weekend as he aims to claim a first-ever major championship and end a six-year wait to win any event.
"I've had a hot putter the last couple of days so try to ride it through the weekend," said the world number 26.
Harman will also have to cope with raucous support behind Fleetwood when the final pairing tee off at 1430 GMT.
Fleetwood, who hails from Southport, just 30 miles (48 kilometres) from Hoylake, is also in the hunt for his first major and aiming to become the first Englishman to lift the Claret Jug since Nick Faldo in 1992.
"If somebody said you're going out in the last group on Saturday, I don't care what the situation was or what anybody had shot, I'd have probably taken it," said Fleetwood, 32.
"That's the way I look at it, and just look forward to playing over the weekend."
Heavy overnight rain has softened up the course to give the chasing pack the chance to close in on the leaders.
Americans Rickie Fowler and Patrick Cantlay were among the early starters and produced four-under rounds of 67 to move to one under par for the tournament.
Defending champion Cameron Smith and Masters winner Jon Rahm also started well to reach one under par.
World number two Rory McIlroy will begin his third round nine off the lead as he targets an end to his nine-year major drought.
The Northern Irishman is aiming to repeat his sole British Open triumph the last time the tournament was held at Hoylake, in 2014.
World number one Scottie Scheffler will not be adding to his sole major at the 2022 Masters.
The American sneaked into the weekend thanks to a birdie at the last on Friday, but a one-over-par round on Saturday pushed him to four over for the tournament.
PGA Championship winner Brooks Koepka is also at four over after a 72.
