The visitors made a fine start when striker Eder fired his 10th goal of the season in the eighth minute after racing onto a fine through-ball from Carlos Carbonero.
But Roberto Inglese seized on a defensive error to equalise for the hosts in the 34th minute and almost put his side in front with a shot that whistled past the post just before the break.
The result leaves Sampdoria in ninth place in the Serie A table while 12th-placed Chievo now find themselves without a win in five games.
Meanwhile, Riccardo Saponara struck the only goal of the game as Empoli overcame Palermo 1-0 away from home in Serie A on Monday.
The former AC Milan midfielder struck the winner in the 53rd minute with a low free-kick from the edge of the box which crept under the jumping wall and into the bottom-left corner.
Victory lifts Empoli to 12th, a point and a place above Chievo who drew 1-1 at home with Sampdoria.
