AC Milan rebounded from Champions League disappointment by beating already-relegated Sampdoria 5-1 in Serie A to boost their bid to qualify for next season’s competition.

Olivier Giroud netted his first Serie A hat-trick, Rafael Leao also scored, while Brahim Díaz set up two goals before capping a fine performance with one of his own in the second half. Leao also set up Giroud's third and won a penalty.

Milan lost at Inter 1-0 on Tuesday in the Champions League semi-finals and was eliminated 3-0 on aggregate.

Leao missed the first leg with a thigh injury and appeared not to be fully fit in the second leg. But he was back to his best on Saturday.

He raced onto a chipped Díaz ball over the top in the ninth minute and controlled it before slotting home. Leao was already smiling broadly before the ball hit the back of the net.

Sampdoria equalised through 40-year-old Fabio Quagliarella, giving him a Serie A goal in 18 straight seasons.

However, Milan restored their lead three minutes later when Giroud headed in Díaz’s cross from a short corner.

Giroud doubled his tally in the 29th by converting a penalty after Leao was brought down by Sampdoria defender Koray Gunter.

Milan didn’t let up after the break and Díaz got on the scoresheet in the 63rd after combining well with Leao and Sandro Tonali.

Giroud completed his hat-trick five minutes later, beating Samp defender Bram Nuytinck to bundle in a cross from Leao.

Atalanta kept alive their hopes of qualifying for Europe by rallying to beat relegation-threatened Hellas Verona 3-1. Atalanta were three points behind Milan.