Bjorn, who won the tournament in 1999, had three birdies on the 6,917-yard, par-71 Phoenix Country Club for a 12-under 272 total.
Japan's Daisuke Maruyama fired a 70 to finish second, two strokes back. Garcia, who had a three-stroke lead heading into the final round, had six bogeys, a double-bogey and just one birdie for a 78 that left him in sixth place -- four shots back.
Britain's Lee Westwood had six birdies for a final-round 66 that left him three strokes back in third place, along with Japan's Tetsuji Hiratsuka and American David Gossett.
After bogeys on Nos. 3 and 4, Garcia got his first birdie on No. 7 but a double bogey on the next hole ruined any momentum he hoped to build.
He missed a 2-foot par putt on the 10th hole for his fourth bogey as Bjorn took the lead for good.
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