Sorenstam and Koch overcame an early two-hole deficit to beat Kim and Yokomine on Tanah Merah Country Club's renovated Garden Course.
'I know Carin really well,' Sorenstam said. 'We grew up together and played a lot of amateur golf together, so today was a perfect pairing.'
The Swedes also have played well together in the Solheim Cup.
'It's a nice security to know that she's going to hit the next shot,' Koch said.
Sorenstam and Grace Park are serving as playing captains.
'All in all, I think all my girls are very happy, very pleased with the result,' said Park, one of nine South Koreans in Asia's lineup.
The teams will play six best-ball matches Saturday and the LPGA Tour-sanctioned event will conclude Sunday with 12 singles matches.
'The Asians played very, very well,' Sorenstam said. 'We had some tough matches coming down to the 18th and it could have gone either way, really. I think that it makes for an exciting Saturday and exciting cup to have the teams so close.'
Young stars Julieta Granada and Morgan Pressel gave the International team another full point, beating Se Ri Pak and Hee-Won Han 4 and 3.
The 19-year-old Pressel ended the match with a spectacular eagle on the par-5 15th, holing out from 122 yards with a 9-iron shot that spun halfway around the cup.
'I had just said to Julieta before, 'Let's end this match on this hole! Let's win this hole!'' Pressel said. 'I didn't make her putt. She was happy.'
The 20-year-old Granada, from Paraguay, earned a spot in the event last month with her $1 million victory in the LPGA Tour's season-ending ADT Championship.
Jee Young Lee and Meena Lee had a big comeback for Asia, overcoming a four-hole deficit at the turn to beat Natalie Gulbis and Paula Creamer 2-up.
'We had quite a momentum shift,' Gulbis said. 'As a team, we were probably 1 under for the day, which is pretty good, alternate shot, but we were pretty disappointed to lose that match. It was a pretty big match for us to lose.'
The South Korean duo took advantage of Jee Young Lee's power game.
'When it came to Jee Young and Paula and they were teeing off against each other, Jee Young has about a 50-yard advantage over Paula,' Meena Lee said. 'On some of the longer holes, we had more birdie chances, so we just stuck with it.
'They started missing a couple of shots here and there and that's when we started picking up our game a little bit. They seemed to get frustrated a little bit. We went on and had a good rhythm after that and it turned out well.
Seon Hwa Lee and Young Kim also earned a point for Asia, routing long-hitters Brittany Lincicome and Laura Davies 6 and 5.
Two matches ended in ties. International players Angela Stanford and Stacy Prammanasudh halved with Grace Park and Shi Hyun Ahn, and Asia's Candie Kung and Jennifer Rosales tied Sherri Steinhauer and Nikki Campbell.
If the teams finish in a tie Sunday, Sorenstam and Park will have a sudden-death playoff to determine the winner. The winning team members will each receive $50,000, and the losers will get $30,000.
Last year, the International team won the inaugural matches 16-8.
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