During another hard-fought race at the 4.023km long circuit in the English Midlands Can Öncü battled for the podium positions in the early laps but dropped back as the race wore on, finishing in eighth position.
An early misfortune saw potential top five rider Montella fall from contention into the first corner, and he was unable to restart.
After strong rides in Race One it was a tough finish to the first ever race weekend for each Kawasaki Puccetti Racing rider at this classic old British venue.
Race Two was held over the full 19-lap distance, unlike the shortened Race One on Saturday.
Leaving the UK, Can is still fourth overall in the championship rankings, now with 99 points in total. Yari is still fifth, with 75 points.
The sixth round of the WorldSBK championships will take place at Most in the Czech Republic, between 29 and 31 July.
Can Öncü, stated: “This English circuit was new to me and a little bit difficult for us. It has a lot of everything you find in racing. We scored points but in some ways it is a weekend we need to forget and look forward to the Czech Republic race weekend.”
Yari Montella, stated: “I'm really disappointed today because without the foolish move of another rider, I could have battled for the podium. But that's racing and there's no point dwelling on it. We need to react and focus on the next round at Most. I'm really sorry for the team too, as they did a great job and I'd have liked to repay them with a good result.”
Adrian Huertas (MTM Kawasaki) finished Race Two in seventh position, making him the top Kawasaki rider on the day. He is tenth in the championship, just three points from the rider in ninth.
Local rider Tom Booth-Amos (Prodina Racing Kawasaki) crashed early in the race but restarted to finish 17th, just outside the points scoring places.
Ben Currie and Jeffrey Buis (Motozoo Racing by Puccetti Kawasaki) finished Race Two in 19th and 20th positions respectively.