Samp suffered only their second defeat of the entire Serie A season.
The 21-year-old Brazilian had never found the net in his first Serie A season, but has now contributed to eight of Lazio’s last 10 goals. Including the Coppa Italia, he has scored five goals in five games.
“We know that we are a great team and are aware of our quality, so we can work calmly,” Anderson told Sky Sport Italia.
“We managed to keep our heads in the first and second half. We are on the right track and must keep our feet on the ground, but we are also aware that we can go far.
“We proved not just today, but from the start of the season, that we have quality. We need to keep going like this.”
After creating the first goal for Marco Parolo and then rifling home a 25-metre shot just before halftime, the inspired Brazilian capped his performance by running 50 metres to lay the third on a plate for Filip Djordjevic.
Although the sides began the match level in joint third alongside Napoli, Sampdoria were ultimately outclassed and seemed certain to get a roasting from coach Sinisa Mihajlovic who watched most of the second half with an angry, fixed stare.
Pedro Obiang summed up their frustration when he kicked away a drinks container in disgust after being substituted in the second half as Sampdoria suffered only their second league defeat of the season.
Lazio broke through seven minutes before halftime when Anderson burst down the left and laid the ball off for Marco Parolo to volley home.
Three minutes later, the 21-year-old, signed from Santos 18 months ago, doubled Lazio's lead with a low, diagonal shot which flew past Emiliano Viviano and into the left-hand corner, his fourth goal in as many Serie A games.
Not content with that, Anderson then ran from his own half, skipped past a couple of tackles and laid the ball off for Djordjevic to tap into an empty goal midway through the second half.
Lazio moved onto 30 points from 17 games, six behind second-placed AS Roma and a further three adrift of leaders Juventus.
Sunday is the Derby