The Croat defender's 46th-minute header from a corner stood out for its simplicity on a night when the Premiership side made beating Third Division opponents look difficult.
Perhaps the arrival of the 22-year-old Sporting Lisbon striker Hugo Porfirio, who will sign for West Ham today for a fee around pounds 800,000, will sharpen the home side's appetite for goals.
Porfirio, who played in the Euro 96 quarter-final for Portugal, was recommended by his international team-mate Paolo Futre, currently out of the West Ham line-up because of a hamstring injury.
After last week's 1-1 draw on the infamous slope at Underhill, West Ham's manager, Harry Redknapp, had said that if his side could not beat Barnet at home they needed locking up.
The jingling of keys was almost audible in the final minutes as West Ham strained in undignified fashion to prevent Barnet earning the equaliser which would have taken the tie into extra time.
In truth, that would have been more than the north Londoners deserved, for all the game efforts of their lone striker Sean Devine.
The pony-tailed striker, who had scored all three goals in his side's 3-0 win over Exeter four days previously gave Bilic and Marc Rieper a run for their money. But West Ham, despite perfecting the art of going nowhere slowly for much of the game, roused themselves to create the only clear chances.
Iain Dowie, with a header which rebounded from the inside of the post two minutes after Bilic's goal, and Julian Dicks, with a 79th-minute free- kick which clipped the top of the bar, might have prevented the awkwardness of the closing minutes.
"These games are a nightmare for Premiership sides," Redknapp said. "You are on a hiding to nothing. No one wanted to see us score four or five goals more than me. But you have only got to look what happened to teams like Everton and Chelsea tonight to see how difficult these matches are."
As in the first leg at Barnet, the bulk of West Ham's urgency was provided by their leggy Australian winger Stan Lazaridis, who gave another enterprising display before being substituted a quarter of an hour from time. It was his corner from which the unmarked Bilic headed home from close range.
The Croat defender, named man of the match, was presented afterwards with a mountain bike as his prize. But his future team-mate Porfirio will not be requiring a similar award, according to Redknapp. "This boy is so quick he won't need a bike," he said. Sounds promising.
West Ham (4-4-2): Mautone; Breacker, Rieper, Bilic, Dicks; Dumitrescu, Bishop, Moncur, Lazaridis (Ferdinand, 75); Dowie, Cottee (Jones, 88). Substitute not used: Shilton (gk).
Barnet (1-4-4-1): Taylor; Pardew; Gale (Campbell, 41), Primus, Howarth, McDonald; Wilson, Codner, Rattray (Hodges, 60), Hardyman (Tomlinson, 30); Devine.
Referee: C R Wilkes (Gloucester).Reuse content