Stefano Pioli's men have not lost since the Serie A season resumed in June, a run of form that has taken them to sixth place and European qualification while securing the coach an extended contract.
January signing Ibrahimovic has been key and proved the star of the show again with his two goals plus an assist for Hakan Calhanoglu - following a VAR review - in a dominant display at the Marassi that concluded with Rafael Leao's well-taken fourth.
Gianluigi Donnarumma saved a penalty in the second half but was eventually beaten by a brilliant effort from Kristoffer Askildsen.
Milan were outstanding from the off and needed just four minutes to forge the opener as Ante Rebic's smart turn on the left created space for a cross that found Ibrahimovic inexplicably unmarked for a simple header.
A second should have swiftly followed, but Theo Hernandez shot straight at Wladimiro Falcone, who bounced back up to steer Davide Calabria's drive clear.
Falcone then got a toe to Rebic's low finish, before he again came to Samp's rescue with a scrambling stop from a scuffed Ibrahimovic effort on the half-hour mark.
The home side somehow made it to half-time just a goal behind and almost capitalised with an equaliser six minutes after the restart as Donnarumma parried Fabio Quagliarella's free-kick and Omar Colley nodded the rebound over.
However, Milan went straight down the other end and deservedly doubled their lead, with Calhanoglu reaching Ibrahimovic's knockdown to thrash home. Referee Fabrizio Pasqua initially perceived a non-existent foul on Ronaldo Vieira by the goalscorer but made amends with a visit to the pitchside monitor.
Now ruthless where they had earlier been wasteful, Milan had a third when Calhanoglu returned the favour and fed Ibrahimovic to shoot through Falcone.
Donnarumma blocked from close range to deny Quagliarella a consolation and Samp still could not beat the goalkeeper even after Simon Kjaer barged Andrea Bertolacci to the ground in the area, with Gonzalo Maroni's penalty saved.
It took a spectacular effort to finally get the better of Donnarumma as Askildsen curled into the top-right corner three minutes from time, far too late to cause Milan major concern as Leao instead restored the three-goal cushion in style in stoppage time.
Milan in fine fettle
Milan will have a watchful eye on Roma's result against Torino later on Wednesday as they may yet be able to leapfrog the Giallorossi on the final day and avoid the qualifying rounds of the Europa League.
But considering how ordinary the Rossoneri have been at times in seasons past, the entertainment of recent performances alone will send supporters into next term on a high, keen to see their side quickly pick up where they are leaving off.
