Basel claimed only their second win of the new
Streller added another in the 33rd minute and although Enrico Schirinzi pulled a goal back three minutes later, Valentin Stocker put the result to bed before the interval.
Basel climb to second in the table, four points behind leaders FC Sion and one ahead of Young Boys, who were 4-1 winners over FC Zurich. Raul Marcelo Bobadilla's double set the ball rolling for the hosts before Josip Drmic replied for Zurich.
However, Alexander Farnerud further extended Young Boys' lead and Raphael Nuzzolo added a fourth to end the challenge of Zurich, who had Burim Kukeli and Henrique Konzen sent off in a bad-tempered finish.
Grasshoppers beat Servette 1-0 with a 52nd-minute goal from Nassim Ben Khalifa.