The Honda Racing rider tucked the front at Druids on the first lap of the Sprint race after qualifying in 11th position.
Irwin started race two from the sixth row of the grid and dropped to 27th after being caught up in an incident on the opening lap.
The Carrickfergus man then fought his way through to 10th by the end of the race, which was won by Scotsman and reigning BSB champion Tarran Mackenzie on the McAMS Yamaha.
Mackenzie was celebrating his first victory of the season after battling back from injury.
He missed the first two rounds of the championship but will now have his sights set on finishing inside the Showdown top eight. The 26-year-old is currently 11th in the championship but is only seven points behind Australian Josh Brookes (MCE Ducati) in eighth place.
Tommy Bridewell finished third in race two on the Oxford Products Ducati ahead of Bradley Ray on the OMG Yamaha.
Saturday’s race winner Jason O’Halloran took the runner-up spot, 1.1s behind team-mate Mackenzie in a reversal of their positions in the 15-lap Sprint race.
O’Halloran has now taken over at the top of the standings by three points from Ray going into race three (16:30 BST).
Irwin remains in sixth position, 14 points ahead of Bridewell.
His brother Andrew crashed out of race two on the SYNETIQ BMW and finished 14th in race one.