Slovakia have 12 points from six games in Group F, two behind England who drew 2-2 away to Scotland earlier on Saturday.
Slovenia, who beat Malta 2-0, are a further point behind in third, followed by Scotland on eight points and Lithuania on five.
The group winners qualify directly for the World Cup in Russia next year. The best eight second-placed teams in the nine European groups go into a playoff round and the winners of those four ties also qualify.
Vaidas Slavickas and Darvydas Sernas had early attempts for Lithuania but the visitors made the breakthrough with a brilliant combination between Hamsik and Vladimir Weiss in the 32nd minute.
Hamsik, surrounded by defenders, still managed to chip the ball into the penalty area where Weiss controlled it, turned and then fired into the net.
Hamsik scored the second himself with a free kick.
Slovakia appeared to be cruising but had to endure a nervy last couple of minutes after Lithuania pulled a goal back when a free kick by Arvydas Novikovas hit the underside of the crossbar and Sernas headed in the rebound in injury time.
Josip Ilicic and Milivoje Novakovic scored in each half to give Slovenia a modest 2-0 win over table-proppers Malta in the group's other game.
(Writing by Brian Homewood in Berne; Editing by Clare Fallon)
