Both players ended 72 regulation holes at the Wentworth Club golf course with totals of 11-under-par 277 and both qualified for the sudden-death playoff by shooting 4-under 68 over the closing 18 holes.
Wilson had a chance to win the tournament but missed his birdie attempt before Jimenez' winning putt.
"This is my 20th season on the (European) Tour and it's a nice present," Jimenez told the BBC in London.
The win puts the Spaniard at the top of the Order of Merit and likely guarantees his third career Ryder Cup berth in September.
Karlsson shot a disastrous 2-over 74 and missed the playoff after his 4-foot birdie putt at No. 18 did not find the cup.