He also surpassed his own NBA record for threes in a season during the game - reaching 288 with months still to go in the campaign.
Curry ended with 46 points, but the game needed clutch free-throws from Andre Iguodala to even make it to overtime. Iguodala was fouled with 0.7 seconds left and hit two free-throws to rescue the Warriors from a hefty fourth-quarter deficit.
Thunder star Kevin Durant finished with 37 points but fouled out in overtime, while Russell Westbrook had 26 points, seven rebounds and 13 assists.
Forward Serge Ibaka had 15 points and 20 boards while Kiwi Steven Adams racked up 10 points and nine rebounds in 28 minutes.
For the Warriors, Curry has assistance from Klay Thompson (32 points) and Draymond Green (14 rebounds, 14 assists, six steals and four blocks).
The Warriors are now an all-time NBA best 53-5, and are on track to break the NBA record for the best record in a season (72-10).