The Hammers midfielder, replacing former club-mate Frank Lampard on the hour, gave goalkeeper Zelic no chance with a crisply-struck right-foot shot in the 82nd minute that swerved round the defensive wall and nestled in the far corner of the net.
It was a rare moment of inspiration in another friendly international disrupted by mass substitutions by both teams. In fact, an incredible 43 different players appeared on the Walkers Stadium pitch and four players - Michael Owen, Emile Heskey (for 15 minutes), Phil Neville and Jamie Carragher - took turns to wear the captain's armband.
The only England player of the starting line-up that coach Sven-Goran Eriksson did not substitute was Hammers keeper David James.
Apart from a long range shot, 12 minutes from the end, that almost caught him out before spinning viciously off his body and away for corner, James had nothing of note to do.
He had no chance with Serbia & Montenegro's equalising goal, netted from close range by Jestrovic on the stroke of half-time after Ashley Cole just failed to scramble the first headed effort off the goalline.
England had taken the lead on 35 minutes, when Steven Gerrard - easily the pick of a lack-lustre England side in the first half - found Owen on the left and then ran on to the six-yard box to turn home his Liverpool team-mate's low cross.
With five substitutions at the break, followed by three more after 60 minutes, it was not surprising that England (and the East Europeans) lacked much cohesion in their play.
But Cole, coming on to play in his favourite position at the top of the midfield 'diamond', behind Darius Vassell and Wayne Rooney, was determined to make an impact and he lifted the 33,000 crowd with several surging runs and, after 75 minutes, a rasping right-foot shot from 20 yards that stung Zelic's palms.
And for the winning goal, it was Cole who won the free-kick from which he scored. A direct run at the heart of the Serbia & Montenegro defence was only thwarted by a reckless challenge from Vidic that cost the defender a yellow card.
A jubilant Cole ran to the touchline to celebrate his first senior goal for his country, whipping off the No.19 shirt on his way.
Joe told Sky Sports afterwards: "It hasn't really sunk in yet - it's a great feeling to score my first goal and I just want the chance to do it again next Wednesday.
"I said to a few of the lads beforehand that I thought I'd score tonight. Luckily enough, I hit the free-kick and it went in."
Now Joe is desperate to play his part in the more important Euro 2004 qualifier against Slovakia at Middlesbrough next Wednesday.
Joe continued: "It's been frustrating but hopefully I've staked my claim for Wednesday night. I've played 10 times for England but I think I've been on the pitch only once at the same time as David Beckham. Whenever I've played for England I've always felt I've done myself justice but now I'd like a chance to prove myself from the off."
Sky pundit Stuart Pearce, now coach at Manchester City, believes in the ability of his former Upton Park team-mate but thinks Eriksson will continue to start Cole from the bench. He said: "He'll hate me for saying this, but Joe is a great substitute to bring on, because he can score you a goal - as he showed tonight."
Ray Wilkins added: "Joe's best position for England is where he played tonight - at the front point of the diamond - but that's also Paul Scholes' position."
The third Hammer in the squad, Trevor Sinclair, watched the game from the sidelines in his England blazer after being ruled out by a dead leg suffered in training.