
The 22-year-old Englishman - who had a share of the overnight lead - looked destined for a day of frustration as he slipped off the pace having played his first 15 holes of the day in one-over-par.
But he reignited his challenge with an eagle at the par-five 16th and then, having missed another eagle putt to win in regulation at the par-five 18th, tapped home for birdie to earn a spot in the play-off with Gallacher and playing partner Gonzalez.
The trio went down the 18th again and a birdie proved good enough for Fleetwood as his rivals both missed putts to make fours.
It was particularly hard on Scotsman Gallacher who, roared on by the home crowds at Gleneagles, produced a superb eagle at 18 in regulation to become the first man to post 18-under.
(GB & Ire unless stated)
-18 T Fleetwood * (won at first extra hole)
-18 S Gallacher
-18 R Gonzalez (Arg)
-17 S Henry
-B Wiesberger (Aut)
Click here for collated scores
That capped a fine comeback from Gallacher who looked to have blown his chances after running up a triple-bogey seven at the 11th, but then hit back with birdies at 14 and 16.
Meanwhile, Gonzalez also nearly won without the need for a play-off as he came within a whisker of holing his bunker-shot at 18 first time around for what would have been an unlikely eagle.
The leaderboard had remained densely packed all day with numerous players hovering in and around the lead.
Things really began to hot up when Austria's Bernd Wiesberger made an eagle at the 16th to move into the lead on his own at 17-under.
He was then joined by Scotland's Scott Henry who finished in style with an eagle at the 18th to join the Austrian at 17-under and post the clubhouse target.
But both would then be eclipsed by the later finishers and had to settle for a share of fourth place.
Argentina's Emiliano Grillo shot a fine closing 66 to end up in a tie for sixth with England's Paul Waring and Brett Rumford of Australia.

Rob Lee assesses how Gleneagles is shaping up ahead of next year's hotly-anticipated Ryder Cup.

Tommy Fleetwood has a share of the lead heading into the final round of the Johnnie Walker Championship at Gleneagles.

Ricardo Gonzalez claimed a one-shot lead at the halfway stage of the Johnnie Walker Championship after a second 65.

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