The timing of the 22-year-old's first Premiership goal, 10 seconds from the end of stoppage time, meant there was no opportunity for the champions to respond.
Mellor, a burly, home-grown striker whose father Ian played for Manchester City, might have joined Sheffield United a fortnight ago. Injuries to Milan Baros and Djibril Cissé ensured the deal was stillborn, a seemingly inconsequential fact that Arsenal now have cause to rue as they trail Chelsea by five points.
"The ball's just dropped and I've just hit it in front of the Kop," Mellor said in time-honoured fashion. His captain, Steven Gerrard, neatly encapsulated a moment his young colleague may struggle to better in his entire career. "Neil's been dreaming of that for years," he said, "and now it has come true."
The only dreams coming true for Arsenal right now are bad ones. Two defeats in 55 matches may not sound like a crisis, but six points from 18 can be regarded as a modest return indeed. In a game of stunning goals, they negated Xabi Alonso's opener through Patrick Vieira, but having otherwise failed to trouble Chris Kirkland, they could hardly argue with Mellor's winner.
Arsène Wenger sought to do precisely that, suggesting that the chance came about more through his side's sloppy defending than any creativity on Liverpool's part. "It's difficult to swallow when a goal starts with a simple kick by their goalkeeper and the ball ends up in your net," the Arsenal manager said.
What has happened to the aura of invincibility that Arsenal presented before Manchester United ended their unbeaten run at 49 matches last month? Wenger still felt there was "not a lot wrong", but added: "We looked as if we were suffering from fatigue, and Liverpool were sharper than us, especially in the first half. We gave a lot playing with nine men [at Eindhoven] in midweek."
Their problems did not end with the defeat. Vieira's booking, for a foul on Alonso, means that he will be suspended for the summit meeting with Chelsea at Highbury on 12 December. Arsenal's loss of momentum arguably began with the loss of the defensive midfielders, Gilberto Silva and Edu. Now they will also be deprived of their driving force.
On this occasion, however, Vieira met his match. Gerrard, foraging behind the lone spearhead, Mellor, was dynamism personified, swerving past opponents, unleashing shots and uniting with Alonso and Dietmar Hamann to see that Arsenal never established ascendancy, even at the height of their second-half rally.
Playing his first home match since early September, Gerrard was denied a penalty after three minutes when Kolo Touré brought him down. He was inevitably behind the first goal following a move that started when Steve Finnan's long diagonal pass was headed by Harry Kewell to Gerrard, whose slide rule pass into the stride of Alonso was followed by a drive from 18 yards that tore beyond Lehmann.
Arsenal drew level soon after the break with their first shot on target. A flurry of short, first-time passes saw the ball worked from Lauren to Vieira to Thierry Henry and back to Vieira, whose nonchalant finish seemed to announce the resumption of business as usual.
A respectable point looked within their grasp as Kirkland pumped the ball forward. Kewell, who otherwise had a wretched game, again played a part by jumping with Sol Campbell. The ball broke to Mellor, who still had the energy, after so much lung-bursting endeavour, to force his way into Anfield folklore.