Jordan Spieth remained firmly on course for victory midway through his third round at The Open, but Rory McIlroy's hopes of regaining the Claret Jug looked to have evaporated on a day of low scoring at Royal Birkdale.

Branden Grace's stunning 62 - the lowest round in men's major championship history - showed what was possible on a calm day in Southport, with Birkdale's beautiful links having been softened appreciably by the previous day's rain.

Grace's record-breaking performance lifted him to four under for the tournament, while Dustin Johnson (64) and defending champion Henrik Stenson (65) were one shot worse off after joining the birdie blitz.

Yet Spieth was able to reach nine under and maintain a two-stroke advantage over playing partner Matt Kuchar, both men improving their overnight scores by three over the front nine.

Brooks Koepka was four off the pace after turning in 32, but McIlroy had fallen away badly after a strong start.

The 2014 champion birdied three of the first five holes to close in on Spieth, only to bogey the seventh and eighth. After a birdie at nine got him back on track, McIlroy then made a double-bogey at the 10th to slide back to one under for the tournament.

There was a slim possibility of the weather worsening in the evening, with an amber warning in place due to lightning 20 miles from Birkdale.