Marusic thumped home Matteo Guendouzi's perfect inswinging cross in the third minute of added time in Rome to ensure victory in Igor Tudor's first match as Lazio coach.
The Montenegro defender's first goal of the season pushed Lazio up to seventh.
Juve, in third, are stuck firmly in a rut after defeat in the Italian capital left them four matches without a win and sliding back towards a battle for a Champions League spot.
Massimiliano Allegri's side have picked up just seven points from their last nine.
Tudor, who won Serie A and B titles over nine years as a Juventus player, will be encouraged by the solid display put on by his team. The former Croatia defender has a tough opening week at Lazio as his side face Juve again on Tuesday, in Turin for the first leg of their Italian Cup semi-final, before the Rome derby next weekend.