Garrido (72) forced the playoff with a birdie on the 18th hole to finish at 15-under 273. Lawrie shot a 5-under 67.
Im not a party person, but I will enjoy this, the 34-year-old Irishman said after his first European Tour win in 175 attempts.
Both players birdied the first playoff hole.
It just feels unbelievable; Im lost for words, Lawrie said. I thought Id had it won and was telling my caddie Dermott to pack up because we have to catch a plane, when he (Garrido) holed that last putt.
Garrido set a course record with a 63 on Friday.
Soren Hansen (69) finished third at 274. Alfredo Garcia-Heredia (68), Miguel Angel Jimenez (71) and David Lynn (66) tied for fourth, a stroke back of Hansen.