Graham took a 3-0 lead through Simon Blake, Dave Barker and Robert Jamieson before Scott Tucker got Oyster off the mark.
Chris Cobb Jnr then moved Oyster within a leg of their opponents.
But Keith John won the next tie to put Graham on the brink of victory.
It wasn’t to be for Arms, though, as Oyster seized the momentum with Jon Macdonald, Ron Albury and Chris Cobb Snr taking the remaining games to win the match.
Raven are among division C’s early frontrunners after they dispatched George & Dragon 5-4.
Shane Plummer, Frank Woodward and Les Weston put George 3-0 up.
But Alan Gaymer, Glen Bremner and Bob Steel restored parity for Raven.
Les Browne made it 4-3 to George but Sean Spillett and Jerry Goddard won the last two legs to bag the points for Raven.
Froddington B claimed a 6-3 triumph over Admiral Drake B in division D.
Paul Lipscombe opened proceedings for Froddington but Jeff Lovelock hit straight back for Drake.
Brian Hughes and Ron Hannan moved Froddington 3-1 up.
But Peter Girvin and Anthony Griffin once again pulled Drake level with their rivals.
It was one-way traffic from there on with Alan Miller and Brian Cohead winning legs for Froddington and Ron Waters claiming a walkover.
Shearer Arms earned their first win of the season in division A as they beat Rose in June B 5-4.
Jon Bramble scored 180 as he took the opener but Shane Williams and Ian Pearce soon had Rose 2-1 up.
Neil Sheppard scored 180 for Rose in the next set but it couldn’t prevent him going down to Shearer’s Robert Blake.
Shearer went 3-2 up courtesy of Paul Wain.
However, Rose regained the lead through Michael Neat and Chris Harradine.
Ricky Udy and Bruce Baker won the remaining sets to give Shearer the victory.
Steve Filby (Jolly Taxpayer C) threw 13 and 17-dart legs, while Charlie Jackson (Admiral Drake B) recorded a 14-darter. Dennis Smith (Admiral Drake B), Paul La Roche (Jolly Taxpayer C) and Frankie Howard (Newcome Arms A) all finished legs in 18 darts.
Trevor Clements (Duke of Devonshire A) hit a 114 game-shot.
Matthew Bolton (Mermaid) and Lee O’Donovan (Jolly Taxpayer C) hit 103 and 101 finishes respectively.
Meanwhile, Barry Steven (Admiral Drake B) and Bob Ketchen (Lord Chichester A) both fired in maximums and Fred Stevens (Barley Mow) scored 165.