The Subaru driver from Portadown just missed out on a podium place to team-mate Jason Plato in race one.
In race two, Turkington was involved in a first-lap crash but he worked his way through the field to take 15th position.
Turkington finished in an impressive third place in the final race despite starting down in 15th place.
The 34-year-old was only half a second behind the race winner, Dublin driver Aron Smith.
After the weekend's racing, Turkington lies sixth in the championship standings, 48 points behind leader Sam Tordoff.
Carrickfergus driver Chris Smiley also had a good weekend on the English circuit.
He finished in fifth position in the Renault Clio Cup, an impressive feat as it was Smiley's racing debut at Rockingham and his first time driving a Clio in wet conditions.
Smiley was making similar progress in race two, running in seventh place, before being hit by Lee Pattison at the second corner.
Although his car did not make contact with the barriers, the incident dropped Smiley back down the field.
Fourteen-year-old Hillsborough schoolboy Dan Harper had mixed results in the Ginetta Junior series.
The rookie finished 14th, seventh and 11th, gaining valuable points in the Rookie Cup to extend his championship lead.
There are two rounds remaining for Northern Ireland's drivers, with the penultimate event at Silverstone taking place at the end of September.
Colin Turkington secured a third-place finish at Rockingham to keep his BTCC title hopes alive.