This marked the second victory on the European Tour for Price, whose last win was at this event in 1994. He lost out on the championship last year when Gary Orr drained a 12-foot eagle at 18.
Price comments on his 2nd Portuguese Open win
'I think I'm relieved more than anything,' said Price, who had four second-place finishes last year. 'I've finished second so many times that I was thinking over the last three holes, I really do not want to blow this. I've found it difficult to win so to get the job done today was very, very pleasing.'
Stephen Scahill, one of the five co-leaders after the third round, tied for fourth with Alastair Forsyth and Ignacio Garrido. The trio finished at 11-under followed by Brett Rumford and Alex Cejka at minus 10.
Price opened with five birdies in his first six holes, but overshot the green at the 7th and took bogey. Birdies at 10, 13 and 14 gave Price the outright lead, but once again he gave the charging field hope when he three-putted the 15th green for bogey.
The Welshman bounced back when he pitched in from the left rough for birdie at 16, followed by his 10th birdie of the round at 17.
Harrington had opportunities to challenge Price.
He missed a 12-foot birdie putt at 15 and then an eight-footer for birdie at 16. The Irishman's bid for the championship ended at 17 when he drove into a bush and after receiving a free drop because he was behind a television stand, failed to make birdie.
'I hit 18 greens and if somebody had told me I was going to play tee to green the way I did, I would have been thrilled,' said Harrington, who posted a 2-under 70 on Sunday. 'I should have had a better score. The four par-5s hurt me badly because I didn't birdie any of them and I reached all four, that was a pity.'
Price vaulted to 11th on the Order of Merit and sixth on the European Ryder Cup point list.
'I want to be a top player,' said Price. 'Winning was a goal and the Ryder Cup was another for this year. It was pleasing to get the job done here.'
Striver, also a co-leader after Saturday's round, birdied three of his last six to shoot a two-under 70 and share second place.
Simon Dyson and David Gilford, the other co-leader after round three, struggled on Sunday. Both shot 2-over 74s with Gilford mixing three bogeys and a birdie. Dyson double-bogeyed the 6th and closed with a bogey at the last. The pair ended up in a tie for ninth at minus 9.
Full-field scores from the Algarve Open de Portugal.