He finished 54 holes at 16-under 200, which matched the tournament record. Paul Lawrie first established the mark en route to victory in 1999. If Quiros can follow in Lawrie's footsteps, it will be Quiros' third European Tour win in as many seasons.
'I have to be honest, today wasn't a great day with the ball-striking,' acknowledged Quiros. 'I holed so many good putts. I missed two or three, but I'm still in contention.'
Overnight leader Louis Oosthuizen overcame a front-nine double-bogey for a round of 3-under 69. He is alone in second place at 15-under-par 201 at Doha Golf Club.
Maarten Lafeber and Henrik Stenson both shot rounds of 6-under 66 on Saturday and share third place at minus-12. Andrew Coltart, who was in second at the start of the third round, only managed a 2-under 70 and is alone in fifth at 11-under 205.
Quiros flew out of the gate on Saturday with three birdies in his first four holes. He added a birdie at the sixth and when Oosthuizen double-bogeyed five thanks to a four-putt, Quiros found himself alone in the lead.
Quiros collected one more birdie on the front nine, at the par-3 eighth, to make the turn in 31. That was after an all-world par by a tree at nine.
Oosthuizen joined Quiros back in first, but Quiros managed to reclaim the lead. Quiros birdied the 13th to grab back the top spot on the leaderboard, but built a small margin late in the round.
Quiros birdied the 16th and 17th holes to go two clear. Oosthuizen also birdied two of his last three, but is still behind Quiros, whose last victory came in October at the Portugal Masters.
'I try to work and be happy, otherwise, discouragement is going to come,' said Quiros.
World No. 2 Sergio Garcia shot a 5-under 67 to vault into a tie for sixth place at 9-under 207. The Spaniard could've been lower, but found water at the 18th en route to a bogey.
'It's disappointing,' said Garcia. 'There's nothing you can do about it. I don't feel like I hit a bad shot. I did make a good move. I hit a lot of good putts.'
Aaron Baddeley (67), Paul Broadhurst (69), Anders Hansen (68), Miguel Angel Jimenez (70), Chapchai Nirat (69) and Lee Westwood (67) joined Garcia seven shots out of the lead.
Defending champion Adam Scott carded his second consecutive round of 2-under 70. The Australian is part of a large group tied for 36th place at 3-under-par 213.