The Montenegrin rifled in to settle a tight encounter and give the Biancoceleste a crucial victory in their battle to qualify for the Champions League, although they struggled in the second half.
Rodrigo De Paul struck the post for Udinese and the Zebrette were the better team after the break, though couldn’t find a way through as Lazio held out for victory.
Lazio made the stronger start and Ciro Immobile came close as he followed up a parry from a long-range Luis Alberto strike, but could only slice wide.
The striker then pulled a header wide from a teasing Marusic cross, as the Aquile enjoyed the majority of the chances in the opening quarter of the match.
Despite earning a succession of corners, Lazio struggled to make them count, with Sergej Milinkovic-Savic’s half-volley from a delivery deflected just past the post.
Udinese’s came close midway through the first half as Rodrigo De Paul’s pinpoint freekick was met by Fernando Llorente, but the Spaniard could only head straight at compatriot Pepe Reina.
However, the Zebrette were undone when Marusic brought a Milinkovic-Savic ball down and cut back into a crowded box before firing into the far corner, via a slight deflection.
Lazio had Reina to thank for rescuing them on the stroke of halftime after a sloppy Lucas Leiva pass allowed De Paul to release Jens Stryger Larsen in the box, but the goalkeeper parried from close range in the final act of the half.
Udinese came flying out of the traps in the second half and De Paul within inches of levelling after playing a one-two with Roberto Pereyra, before firing against the foot of the post from outside the box.
Meanwhile, Ilija Nestorovski was unable to get a clean connection at the back post from De Paul’s cross, as the hosts dominated the second period.
At the other end, Immobile had the chance to settle the match as he raced clear but could only fire at Juan Musso, before slicing the follow up against the outside of the post.
With just minutes remaining, a magnificent De Paul rabona cross found Stefano Okaka in front of goal the ex-Roma striker nodded over the crossbar, squandering Udinese’s best late chance and condemning them to defeat.