Laverty, on the factory Aprilia, upstaged Briton Tomy Sykes (Team Kawasaki) in both races. A third and a second, however, saw Sykes earn some breathing space in the championship.
In both heats Sykes came home ahead of closest rival Sylvain Guintoli on the factory Aprilia.
Laverty won race one ahead of Marco Melandri (BMW Motorrad GoldBet) and Sykes with Guintoli fourth and Davide Giugliano (Althea Aprilia) fifth.
Guintoli was third behind Laverty and Sykes in race two. Melandri was fourth and Chaz Davies (BMW Mottorad GoldBet) fifth.
It was another disappointing day for South African riders. Four of them lined up in the Supersport race with the best result a 10th place for Ronan Quarmby on the ProRace Honda.
Matthew Scholtz, on a Suriano Suzuki, was 17th with Dave McFadden 24th on a PTR Honda.
Sheridan Morais(Goeleven Kawasaki) was among the retirements in a race won by local favourite and three time world champion Kenan Sofuoglu, much to the delight of Istanbul Park fans, on a MAHI Kawasaki.
Second was Sam Lowes (Yakhnich Yamaha) with Michael van der Mark completing the podium on the Pata Honda.