West Ham United 2 Fulham 2
But the substitute's late, late leveller against ten-man Fulham was still not enough to lift Zola's stuttering 19th-placed side out of the bottom three.
At the interval, West Ham looked to be cruising to victory thanks to Carlton Cole's fourth goal of the season and the dismissal of Kagisho Dikgacoi but a stirring second-half fightback saw Fulham gain the upper-hand, thanks to Danny Murphy's penalty and Zoltan Gera's strike.
Following Monday evening's defeat at Manchester City, Zola had declared that this London derby was like a cup final for two teams already languishing in the drop-zone.
With his side looking for their first Premier League win since the opening day of the season, the Hammers boss made two changes as Zavon Hines and skipper Matthew Upson came in for Radoslav Kovac and substitute Manuel Da Costa.
West Ham, lining up in an attacking, adventurous 4-3-2-1 formation, certainly looked to have heeded their manager's message and, inside the opening minute, lone striker Cole volleyed inches over from 20 yards.
Fulham, who kicked off just one place higher in 18th-spot, had made half-a-dozen changes following Thursday evening's Europa League win over FC Basle as Gera, Dikgacoi, Brede Hangeland, Aaron Hughes, ex-Hammer John Pantsil, and Diomansy Kamara were each recalled to the side.
And with 15 minutes on the clock, Roy Hodgson must have been questioning his decision to bring back Hangeland.
After seeing the Norwegian booked for hauling down the overlapping Julien Faubert, the Fulham boss could only look on in horror as Alessandro Diamanti floated the consequent right-wing free-kick into the near post, where Cole soared above the six-foot, five-inch, Hangeland to head the Hammers into the lead.
Just a minute later, James Tomkins almost doubled the advantage, when he met Diamanti's corner with a downward header that bounced just inches wide of the base of Mark Schwarzer's right-hand post.
In reply, Andy Johnson slid a quick free-kick inches wide as the statuesque home defence looked on and then the toiling Kamara tested Robert Green with a 20-yard stinger.
But six minutes before the break, Fulham's impetus was stifled when Dikgacoi angrily locked horns with Scott Parker and, after the Hammers midfielder was handed a suspension-inducing fifth booking of the season, referee Phil Dowd then dismissed the shocked South African, who was making his first Premier League start.
Hines, Diamanti and Luis Jiminez each tried to demolish the Cottagers before the finish of a first half that West Ham simply did not want to end, but any thoughts they had of coasting through the second half were soon scuppered.
Indeed, within seconds of replacing Johnson with Chris Baird for the restart, the ten men found themselves level, when Upson was adjudged to have hauled down Kamara and man-of-the-match Murphy coolly sent Green the wrong way with the consequent spot-kick.
Things got even worse as the hour-mark approached, when ex-Hammer Paul Konchesky floated over a deep corner which the red-faced Green mis-punched and the gobsmacked Gera beat Herita Ilunga at the far post to send the Fulham fans among the East End crowd of 32,612 wild with delight.
By now it was hard to distinguish which side was one man short and Zola responded with a double substitution that saw Valon Behrami and Stanislas replace Parker and Hines for the final 20 minutes.
Stanislas and Faubert each tested Schwarzer, while Clint Dempsey forced Green into a full-length save before departing with a shoulder injury but the real pain was yet to come for Fulham.
In the second minute of stoppage time, Stanislas unleashed an 18-yarder that took a deadly deflection off Hughes on its way to wrong-footing Schwarzer and giving relieved West Ham a fortunate share of the points.