Eder stepped up to the spot, and he made no mistake with a low effort into the bottom corner that sent the keeper the wrong way.
Muriel doubled their lead midway through the first half as he drove into the box and tricked his way past his marker, before firing a strike beyond the keeper.
Sampdoria were in complete control and 10 minutes later Muriel grabbed his second of the night with a powerful strike into the far corner from just inside the box.
It got even worse for the visitors as two minutes later Eder scored the Blucerchiati's fourth of the evening with a low drive that squirmed under the grasp of the keeper.
The hosts continued to create chances at will, and in the 37th minute they scored again, as Fernando curled a free kick into the top corner.
A minute later the visitors were finally given something to cheer on their Serie A debut, as Andrea Lazzari took down a long ball from Gabriel Silva on the edge of the box, before poking a low strike into the bottom corner.
The second half failed to live up to the excitement of the opening 45 minutes, but David Ivan was sent off for the hosts after picking up a second booking.
Carpi then pulled another goal back with three minutes left to play, as Ryder Matos fired a powerful drive into the far corner of the net.
The visitors almost scored a third in stoppage time, but Lazzari's penalty was saved by Emiliano Viviano, as Sampdoria eased to a comfortable win.