Tournament host Greg Norman and Bubba Watson were a stroke back, and defending champions Jerry Kelly and Rod Pampling opened with a 66 on the Norman-designed Tiburon Golf Club course.
After a best-ball round Saturday, the event will finish Sunday with a scramble.
The teams of Scott Hoch-Kenny Perry, Steve Elkington-Scott McCarron, Anthony Kim-Mark O'Meara, Charles Howell III-Nick Price, Brad Faxon-Justin Leonard and Chris DiMarco-Camilo Villegas opened with 68s. Zach Johnson and Stewart Cink had a 69, and Fred Couples and John Daly were last in the 12-team event after a 70.
Funk, one of the more accurate drivers in golf, and Sluman, known for his strong iron play, made for a perfect pairing in the modified alternate shot, the more difficult of the three formats in the unofficial PGA TOUR event.
'After the start we had, we didn't really feel down about anything, but just kept plugging along, plugging along, and finally the tide turned and we started hitting it close,' said Funk, a winner this year on both the PGA TOUR and Champions Tour.
'If I didn't have Fred as a partner, I would probably still be on the second hole looking to make a triple bogey or something,' said Sluman, the tournament winner with Hank Kuehne in 2003 and 2004. 'He's the all-time great partner. You know he's going to drive it in every fairway out here, and he did.'
Funk and Sluman, a rookie this year on the Champions Tour, overcame a poor start. They were 1 over after five, and Sluman had to make a 6-footer to avoid a double bogey on No. 3. But Funk slid in an 8-foot birdie putt on No. 6.
'I just barely limped one in the hole,' Funk said.
That started a run where the two played the final 13 holes in 9 under. Sluman hit the approach shot and Funk made the putt on Nos. 6, 7, 8, 11, 14 and 17, and they switched it with Funk's approach on Nos. 12, 13 and 16.
Calcavecchia, playing in his 14th Shootout, and Austin, who had never been invited to an offseason tour event before, stayed out of trouble and birdied six of the final nine holes and just missed on a couple of others.
'We were in such good shape every hole,' Austin said.
Norman, who has won his own event once, and Watson birdied Nos. 14, 15 and 18 to get within a stroke.