The 30-year-old had two bogeys in the final round, his first of the event, but compensated with five birdies to win the Spanish tournament with a 22-under-par 266.
Garrido made a valiant effort to catch Poulter by shooting a six-under 66, but only succeeded in moving from ninth to the tournament's runner-up position.
Phillip Price was third with a 16-under 272 for his fourth Top 10 finish of the year and likely succeeded in completing his goal of cracking the world's top 50 players.
"I have played as well as this all year," he said. "I haven't done anything different this week apart from roll a few putts in and I have won comfortably. It's all about getting the ball in the hole and I have done that very nicely this week."