Graeme McDowell trailed entering the closing stretch, and birdied the 16th, got up and down from a bunker at the short 17th and then almost eagled the 568-yard last - leaving Karlsson, in sand for two, needing to hole from eight feet for a half. Which Karlsson missed.
“One down with three to play against a great player, I feel very fortunate,” said the Northern Irishman, who now meets South African Jbe Kruger.
Brandt Snedeker began his opening group game with just 10 clubs in his bag and yet won the first three holes before more arrived.
Snedeker was forced to seek replacements when his usual set went missing en route from Florida on Monday. They eventually showed up at Malaga Airport this morning, then were driven to Finca Cortesin an hour away and taken to him on the fourth tee.
Under the rules he was allowed only to add four to those he had started with, but was so happy with the driver he had borrowed from Australian John Senden and the putter he had chosen in the pro shop that he continued with them.
“The driver worked really well, so I think it’s mine now and no longer his,” said the three-time PGA Tour winner, who hopes to use this week to impress American Ryder Cup captain Davis Love.
“It was kind of a weird day to say the least. I didn’t like my chances at all actually. I knew Thomas was a world-class player and it was pretty windy, so I knew it favoured him.”
Bjorn, though, has been suffering from a virus lately that forced him out of the last two events in America, and he could never recover from bogeying the opening three holes, falling five down after six and losing 5&4.
It was not the biggest defeat of the day, however. Robert Rock crashed 7&6 to fellow Englishman Justin Rose, who birdied the first five holes, winning four of them, and later added two more.
The week is not yet over for Bjorn, Rock, Karlsson and the other four who lost on the opening day - Sweden’s Peter Hanson, Senden, Alvaro Quiros and top seed Martin Kaymer - under the revised format of the famous event.
They could yet make it through to the last 16 if they win their second games. Ian Poulter won the title last year after failing to win either of his group matches - he halved them both.
Second seed Rose said: “The game was good, I adjusted to the speed of the greens quickly and Robert didn’t.”
To guarantee himself a place in the knock-out stages Rose now needs only a half against British Open champion Darren Clarke, the lowest-ranked player in the group after his slide to 70th in the world.
The same applies to Poulter against Tom Lewis, the 21-year-old who led the Open as an amateur last July and then won the Portugal Masters on only his third professional start.
Scot Paul Lawrie started his 500th European Tour event with a 2&1 victory over the higher-ranked Hanson, winning the 16th with a par to go one-up and then making birdie from five feet on the next after his six-iron tee shots kicked off the bank right of the green.
Lawrie and Hanson now have to play Colombian Camilo Villegas, while Kaymer lost 3&2 to Dubai Desert Classic winner Rafael Cabrera-Bello and Spain’s other winner was Sergio Garcia, who came from behind to beat compatriot Quiros 2&1.
There was also one halved game, last year’s Masters champion Charl Schwartzel making birdie on the last to square things against last year’s surprise semi-finalist Nicolas Colsaerts.
