Garrido's second place earned him 83,320 Ryder Cup points and sent him up from 16th to 10th place in the Cup table. Harrington, joint sixth, collected 24,375 points to remain in 11th place as the pair sent Jose Maria Olazabal tumbling from 10th to 12th.
Ballesteros needs Olazabal in the top 10 to prevent picking two men from the Spaniard, Nick Faldo and Sweden's Jesper Parnevik at the end of this month when the European team will be decided.
Even Haeggman, who shot 69 for a 72-hole aggregate of 270, now thinks he has a chance of getting into the top 10.
The tall Swede has moved up from 41st to 17th in the Cup table with his first prize of pounds 125,000 and said: "Two weeks ago I hadn't a hope of making the team. Now I'm not so sure."
Garrido, however, made the most important move for he is now more than 14,000 points ahead of Harrington with only four counting tournaments still to play. The 25-year-old said after his 67: "I think I will make the team now. I don't feel any pressure and you cannot imagine how much my mind has changed since I won the German Open in June. I have so much more confidence now and I am so pleased I am so close to making the Cup team."
Garrido has an even greater incentive than his rivals to play for Europe for if he does he will follow his father, Antonio, who played in the 1979 Ryder Cup match at Greenbrier, West Virginia. They would then become the second European father and son combination after Percy and Peter Alliss to earn the distinction.
In Castle Rock, Colorado, Phil Mickelson moved within sight of a second career Sprint International title on Saturday by taking a healthy five- point lead into the final round.
Mickelson compiled six birdies in a bogey-free six-under-par 66 round on the soggy Castle Pines course to pick up 12 points under the modified Stableford scoring system being used for the event. The format awards five points for eagle, two for birdie, zero for par, minus one for bogey, minus three for double-bogey or worse.
The former US Amateur champion had 39 points with one round left, a tournament record low total for the first 54 holes. That put him five points clear of Skip Kendall, while long-hitting Australian Stuart Appleby trailed by seven points.
Scores, Digest, page 19