Hamsik began his professional career at the Slovakian club but showed no sentimentality when he headed his side ahead in the first half and then set up substitute Gonzalo Higuain to double the lead with only his second touch after the break.
Holders Sevilla needed a 90th-minute equaliser from Stephane Mbia to rescue a 2-2 draw at Croatian side Rijeka in Group G having been reduced to 10 men in the second half.
The Spaniards took the lead through Liverpool loanee Iago Aspas, but Timothee Kolodziejczak was sent off for bringing down Andrej Kramaric, who fired in the resulting penalty and Zoran Kvrzic then put the hosts 2-1 ahead.
It was a disappointing night for former European champions PSV Eindhoven, beaten 1-0 at Dynamo Moscow in Group E, and Steaua Bucharest, who lost 3-1 at Dynamo Kiev in Group J.
There was better news for another former European Cup winner Feyenoord, who won 2-1 at home to Standard Liege in Group G.
Everton's Samuel Eto'o scored a late equaliser to secure a 1-1 draw at Russian side Krasnodar in Group H where Kevin de Bruyne netted a superb volley as VfL Wolfsburg drew 1-1 with Lille in Germany.
