The visitors extended their advantage above the bottom three to four points with a victory which was built upon clinical finishing, although Cagliari will bemoan their misfortune after twice hitting the post.
Paloschi grabbed the opener midway through the second period and Thereau sealed the points with a stunning free-kick three minutes from time.
The Veronese started with intent and Perparim Hetemaj came close to giving them a fifth-minute lead but dragged his shot wide from inside the area.
Cagliari responded with Davide Astori playing in Mauricio Pinilla but the Chilean also failed to hit the target.
The hosts remained on the front foot, with Andrea Cossu shooting high over the bar after 26 minutes before Chievo goalkeeper Stefano Sorrentino was forced into action to keep out a Daniele Conti drive.
Sorrentino also excelled in first-half injury time, denying Marco Sau low to his right.
Cagliari continued to press but the woodwork denied them eight minutes after the restart, with Francesco Pisano's shot coming back off the right post with Sorrentino beaten.
The woodwork also denied Sau from close range nine minutes later.
Chievo rode their luck and went ahead after 67 minutes, with Hetemaj crossing for Paloschi to head in from inside the six-yard box.
The goal deflated Cagliari who, a wayward Pisano shot aside, rarely looked like finding an equaliser.
And Chievo finished them off late on with a wonderful Thereau free-kick which flew into the top corner.