Sven Struver (65), Simon Dyson (67), Stephen Scahill (66) and David Gilford (69) joined the Irishman at the top of the leaderboard.
Niclas Fasth and David Howell are tied for sixth at 10-under while Roger Wessels, Ignacio Garrido and Ricardo Gonzalez are at minus 9.
Harrington started well with birdies at the 2nd and 6th for a front-nine 34, but he missed a three-footer for par at 11. He reached the green in two at the par-5 12th but again three-putted for par.
The Irishman rebounded with an eight-foot birdie at 13, but pulled his drive on the 17th tee and took bogey on the hole which he birdied in both of the previous rounds.
'Obviously, it is my highest score in the easiest conditions, but I was still quite happy with the way I hit the ball,' said Harrington, who has never won a tournament where he owned a piece of the lead after the first round.
'I suppose I missed a bit of an opportunity out there today. If I'd shot 5 or 6-under like some of the other guys, then the tournament would be in my grip.'
Struver had the low round of the leaders with a bogey-less 65. He carded three birdies in a row, starting at 11 and then punctuated his round with a birdie at 17.
The German will be looking for his fourth win on the European Tour.
Dyson, the winner of last year's Asian PGA Tour Order of Merit, posted four birdies and a bogey at the 15th. He rebounded with birdies at 16 and 17 for his 5-under 67.
'Now I've got myself into this position, I'd like to think I can capitalize on it,' said Dyson. 'A top-10 spot would be nice and if I finished the top-three, I'd be over the moon.'
Scahill was lucky on Saturday, as his drive at No. 8 nearly went out of bounds. He was able to scramble for par and a 66, including four birdies in his last seven holes.
'My drive was terrible and hit a tree and flew towards the out of bounds,' said Scahill, referring to the 8th. 'There was also a big bush about three feet from where my ball landed so I really could have taken seven or anything on that hole.'
Gilford caught Harrington early but a poor recovery shot at 15 cost him a bogey and the outright lead.
He will be in search of his first win on the European circuit in seven years.
Full-field scores from the Algarve Open de Portugal.