Tiger Woods rolled back the years in thrilling fashion to revive hopes of a 15th major title as the 147th Open Championship exploded into life.

Woods has not played in the Open since 2015 due to injury and is without a victory since 2013, while the last of his 14 major titles to date came a decade ago in the US Open.

But the 42-year-old has made a remarkable return to action since undergoing spinal fusion surgery last April, and a third round of 66 at Carnoustie certainly had his legion of fans believing in what had once seemed impossible.

ā€œItĀ seemed like everybody was shooting six, seven under and I figured I could probably do the same and I needed to with the leaders starting at six. I need to go get it,ā€ Woods said.Ā ā€œItā€™s one of my better rounds Iā€™ve played. I felt I really had control of the ball.ā€

Starting the day six shots off the lead after two rounds of 71, Woods birdied the fourth and sixth before holing from 40 feet for another on the ninth to reach the turn in 33.

A brilliant approach to the 10th set up a tap-in birdie and despite looking unconvincing with the driver, the former world number then unleashed a superb tee shot on the 11th which finished just a few feet left of the green.

From there Woods two-putted from long range for another birdie and when he did the same on the par-five 14th, he was tied for the lead in a major championship for the first time since the second round of the 2013 Masters.

A bogey on the 16th halted the charge but Woods enjoyed a massive slice of luck on the 18th, where his tee shot seemed destined to find the Barry Burn only to take a fortunate bounce to the right to stay on dry land.

After pitching back on to the fairway Woods hit a superb third shot to two feet to crucially save par and finish a shot behind clubhouse leader Francesco Molinari, who carded a flawless 65.

Former champion Zach Johnson and compatriot Kevin Kisner were setting the pace at eight under par midway through their rounds, with defending champion Jordan Spieth a shot behind.

ā€œIt kept me in the fight,ā€ Woods added. ā€œIf the guys get to 10 (under), five back is certainly do-able. I didnā€™t want to drop that last shot.Ā I played so well today I donā€™t feel like I should have shot four under.ā€

Englandā€™s Justin Rose is a shot behind Woods after earlier equalling the lowest score in an Open at Carnoustie with a brilliant 64.

Rose, who finished fourth in the Open as a 17-year-old amateur 20 years ago, birdied the 18th hole on Friday evening to make the halfway cut with nothing to spare on three over par.

And the Olympic champion carried on where he left off on Saturday, taking advantage of benign conditions to fire seven more birdies to match the 64s recorded by Steve Stricker and Richard Green the last time Carnoustie staged the Open in 2007.

ā€œIt was massive to take advantage today,ā€ Rose said after the lowest score of his career in any major. ā€œI was very excited last night not to be down the road, ruing another OpenĀ opportunity gone. I picked up where I left off and it was a greatĀ dayā€™s work.ā€