The home side came into this meeting in Rome locked on 27 points, along with their opponents and Napoli in the battle for third place.
This comprehensive victory earns them a three-point cushion, although that advantage could be short-lived with Napoli travelling to struggling Cesena on Tuesday.
Marco Parolo opened the scoring for the home side in the 38th minute, blasting a volley into the net after being picked out by Felipe Anderson who had burst away down the left.
Anderson then grabbed one for himself three minutes later as Lazio continued to assert their dominance.
The Brazilian thumped a sweetly-struck shot into the bottom corner from outside the box, for his fourth goal in as many league appearances.
And it was Anderson who had a hand in the third goal midway through the second half, teeing up Filip Djordjevic as any hopes of a Samp comeback were extinguished.
