During a cagey opening 15 minutes, Isaac Baird fired just off target from the edge of the box.
At the other end, smart defending from Chris Shields thwarted Enrique Esono's attempted counter-attack after Linfield failed to take advantage of a corner.
On 29 minutes, the home side had the best chance of the first half when the unmarked Oleksandr Musolitin gained possession at the edge of the box, but his low shot was inches wide of the left-hand post.
Chances remained at a premium, but Linfield grew in confidence as the half progressed with Matthew Fitzpatrick's effort gathered by Henri Perk and Darragh Leahy's header just wide.
Just before the half-time whistle, Enrique Esono could not test Chris Johns and fire Kalju ahead against the run of play.
The home side broke the deadlock just after the restart when Vukusic converted Musolitin's corner after some slack defending.
Kyle McClean had a chance to level the game almost instantly when he burst into the box, but he could not keep his strike on target, to the frustration of the travelling fans.
On the hour mark, Kirk Millar's skilful delivery to the back post could not be steered home by Darragh Leahy.
Substitute Kieran Offord caused the home side's defence problems after his introduction with his effort from the edge of the box saved by stopper Perk.
In additional time, the busy stopper also denied Ethan McGee's corner before Mihhail Orlov's curling effort struck the woodwork.
Despite both sides pushing until the final whistle, Linfield could not find a leveller before an intriguing second leg in Belfast.