Warren got away with hitting his drive into the woods at the first playoff hole -- the par-four 18th -- when Karlsson also made a bogey from a greenside bunker.
Back at the 18th for the second extra hole, Warren found the fairway with his drive. This time it was Karlsson who knocked his tee shot into the woods, and it only got worse for the Swede when his second hit a tree.
Warren, meanwhile, knocked his approach within 15 feet and two-putted for his first career European Tour victory.
'It's a fantastic feeling at the moment,' said Warren, who shot 3-under 69 in his final round to end alongside Karlsson at 10-under-par 278 for the tournament.
Karlsson closed with a 1-under 71 and became the second Swede in as many years to lose in a playoff in front of his home crowd (Mark Hensby beat Henrik Stenson last year).
It looked for a while like Karlsson, after setting a course record with a 63 on Saturday, might run away with the title Sunday. But he actually ended up scrambling for the tie by making a bogey putt from the fringe at the 17th hole.
Moments earlier, Warren had birdied the 18th to get to 10 under. It was the last of three birdies for Warren on a spotless back nine.
Then, Karlsson knocked his approach from the rough at the 18th to within 12 feet, but came up short on his birdie putt, forcing the playoff.
Battling a cold, Karlsson was seeking his second consecutive title after winning the Players Championship of Europe last week.
'It's been a strange week,' Karlsson said. 'After two days I was halfway back to Stockholm, so second isn't too bad a week after a win.'
Warren, a rookie, was No. 1 on the European Challenge Tour last year. He gained inspiration Sunday from previous accomplishments.
'The Walker Cup and the Challenge Tour told me I can handle pressure,' said Warren. 'It just seems I look forward to pressure situations. I don't seem to have any fear of what can go wrong. I've got the belief that under pressure I can conjure something up. Maybe I was born with it.'
Richard Sterne of South Africa shot a 3-under 69 and finished alone in third place, one stroke back at 9-under-par 279. Marcel Siem was fourth at 8 under following a final-round 68.
Behind Karlsson, Peter Gustafsson was the highest finisher among the Swedes in the field. He shot a 72 and shared fifth place with Raphael Jacquelin (70) at minus-7.