Two-time U.S. Open winner Retief Goosen posted a 68 to join Thomas Levet and reigning Masters champion Phil Mickelson in a tie for third at 6-under-par 207.
Barry Lane was one shot further back at 5-under-par 208. Tiger Woods followed, after a round of 68 left him alongside Scott Verplank in a tie for seventh at 4-under-par 209.
Hamilton traveled the world for the first 17 years of his career, becoming a multiple winner in Japan before finding success on the PGA Tour earlier this season with a victory at The Honda Classic.
The 38-year-old played alongside Els on Saturday. While both have competed around the globe, Els has been to greater heights in the world of golf. But in the third round, Hamilton surpassed his playing partner to take the lead heading into the final round of a major championship.
'To be honest, I never even considered contending or not even too much playing in the majors,' said Hamilton. 'I just tried to improve on my golf game in Japan, tried to become more patient with my game, improve on the things that I needed to do and somehow get to the U.S. tour. I really didn't look at the majors as an ultimate goal. My goal was to get on the PGA Tour. It took me quite a long time.'
Hamilton parred his first three holes before reaching the green at the par-5 fourth in two. Hamilton missed his eagle try, but ran home his birdie putt to get to 5 under. At the par-4 sixth, Hamilton's birdie putt curled into the hole and he was on his way up the leaderboard.
He added a birdie at the eighth to keep pace with Levet, who was coasting at 9 under after a solid front nine. After Levet three-putted for a double-bogey at the 11th, Hamilton found himself in a tie for the lead at the British Open.
Hamilton was steady on the difficult holes on the inward half, safely hitting greens and lagging long putts close to the hole for easy pars. At the par-4 13th, Hamilton knocked his tee shot inside 3 feet for his fourth birdie of the day to take the outright lead at 8 under.
Lane joined Hamilton in the lead with a birdie at the 15th, but the veteran Englishman found trouble with a double-bogey at the 17th to fall back to minus-6.
Hamilton's tee shot to the 17th rolled off the green into the rough, but he got up-and-down for a par. He then parred the last as the wind began to pick up down the stretch to secure the 54-hole lead with a chance to follow in the footsteps of Ben Curtis and become the second straight first-time major winner at the British Open.
'I don't see why it couldn't happen again,' Hamilton said. 'I'm sure at the start of the week you wouldn't think something like that could happen.'
While Hamilton will assume the roll of front runner on Sunday, he has a leaderboard packed with some of the biggest names in the sport biting at his heels, including the man who will be his playing partner for the second straight day at Troon.
'It's a pretty good leaderboard, isn't it?' said Hamilton. 'Names you would expect at a major championship.'
Els, who survived a four-way playoff to win the British Open in 2002, dropped his approach inside 7 feet for a birdie at the opening hole. He then played his second shot to 6 feet at the sixth to move within one of the lead.
His tee shot to the difficult par-3 eighth found a bunker and Els was unable to save par. Els dropped another shot with a bogey at the 11th to fall back to minus-4.
With plenty of major experience at his side, Els persisted and hit his second to 5 feet for a birdie at the 13th. Els then drained a 13-foot putt for a birdie at the 15th and two-putted for a birdie at the 16th to again move within one of the top spot at 7-under-par 206 after a round of 68.
'Going into the final round you need to be patient, have confidence and have staying power because you know that not everything is going to go your way,' said Els. 'The course gives and it takes so you just have to hit your shots and try your best.'
Mickelson came close to winning the U.S. Open last month and now the left-hander once again finds himself in contention at a major.
He hit a bad drive in the mist at the first that actually found the rough on the 18th hole. Mickelson played a remarkable shot that landed within 6 feet of the cup and what could have been a disaster turned into an early birdie.
Mickelson, who has never finished in the top-10 at the British Open, added a birdie at the very next hole and dropped his approach inside 6 feet at the par-4 seventh for another birdie to grab a share of the lead at minus-6.
The 34-year-old was unable to pick up a birdie the rest of the way and parred his remaining holes for a 68.
'It is nice not to give shots back,' said Mickelson. 'It doesn't feel like they've been overly difficult pars.'
Goosen, who knocked off Mickelson at Shinnecock thanks to a superb putting display, had a fruitful start despite a pair of bogeys on the front nine.
The South African birdied three of his first six holes and ran home a 15-foot putt for a birdie at the ninth to make the turn at 5 under. Goosen mixed two birdies and a bogey on the back nine to finish two shots off the pace.
Levet began the day one behind Skip Kendall, but the Frenchman soon moved into the lead a birdie at the third and back-to-back birdies from the fifth that lifted him to 9 under.
The 35-year-old struggled on the back side, however, with a double-bogey at the 11th and a bogey at the 16th to complete a round of 71.
After two straight birdies starting at the 12th, Lane hit his second shot to 7 feet and rolled in the putt to match Hamilton at 8 under. He also found trouble down the stretch, however, with a double-bogey at the 17th and a bogey at the last to finish three shots off the pace.
Woods made a charge early as a squall came across from the Firth of Clyde and settled in over Troon. The top player in the game birdied his first two holes and reached the green in two en route to a birdie at the par-5 fourth.
'It was a good start,' said Woods. 'I just tried to take advantage of that front nine.'
The 28-year-old then converted a 10-foot putt for a birdie at the seventh and saved par at the eighth to keep his momentum. Woods picked up a clutch par save at the 10th, but the top player in the struggled to a bogey at the 12th to fall four shots back.
Local favorite Colin Montgomerie managed a 1-over 72 to join Kendall and Mike Weir in a tie for ninth at 3-under-par 210. Nick Price, the 1994 champion at Turnberry, was one shot further back along with Lee Westwood and K.J. Choi at 2-under-par 211.