Trailing third-round leader Campillo all afternoon, Finland's Välimäki finally hit the front at the 17th courtesy of a seven-foot birdie putt.
But the pendulum swung back Campillo's way as the Spaniard birdied the last to join Välimäki on 18 under par and take the contest to extra holes.
And Välimäki only needed one play-off hole to seal victory, as a nerveless birdie putt earned him a second DP World Tour title.
Scott Jamieson wrapped up his card for next season with another stunning back-nine display at Doha Golf Club, signing for a closing 69 to finish in a tie for third alongside Nacho Elvira on 16 under.
Välimäki went into the final round one shot behind leader Campillo but found himself two back straight away after his playing partner birdied the first for the fourth round in succession to get to 17 under.
And the 25-year-old appeared in danger of being cut adrift after dropping a shot at the sixth.
But he responded with back-to-back birdies on the seventh and eighth, holing from around 15 feet on both occasions.
He cut the gap at the top to one shot with an 11-foot birdie at the 12th, before pulling alongside 2020 champion Campillo with a 20-foot putt on the 13th, with the Spaniard narrowly missing his birdie attempt from 13 feet moments later.
Campillo came agonisingly close to getting a birdie on the next hole but his 16-foot effort clung to the left edge of the cup without dropping.
But no damage was done as Välimäki failed to take advantage from a little closer in.
Errant tee-shots from both of the leaders at the 15th threw the battle wide open, with Välimäki among the pebbles and Campillo in the thick rough.
While Välimäki opted to knock his ball back onto the fairway, Campillo went for the green and managed to two-putt from 40 feet for par, while the Finn surrendered a bogey after missing his 20-foot par try.
But it was Campillo's turn to find the rocks with his tee-shot at the 16th, and he made his first bogey of the day to sit alongside Välimäki on 17 under.
Both players found the green at the short 17th, but after Campillo's 13-foot putt pulled up just shy, Välimäki holed from seven feet to take the lead for the first time all afternoon.
The momentum swung back Campillo's way on the 18th as he found the green in two, while Välimäki had to lay up. With Välimäki only managing a par to sign for a closing 69, Campillo tapped in his birdie putt from close range to post a 70 and take the contest to a play-off.
But Välimäki came out on top at the first extra hole, knocking in his birdie putt from around six feet after Campillo had missed his attempt.
An emotional Valimaki was thrilled with his victory, saying: "Unbelievable. It's hard to talk. It's been a long journey and it feels great.
"I've worked so hard and I feel like I've earned it a couple of times but it hasn't come my way. That's why it feels so amazing."
When asked what it meant to have his fiancée present for his victory, he added: "She is my number one."