Booed throughout for his alleged part in an injury sustained by a Walsall reserve player during his Carlisle days, Hayward powered the sweetest of rising drives beyond the goalkeeper James Walker with two minutes remaining.
Walsall, who led twice through Rob Steiner and Ian Roper's first League goal either side of Jamie Smith's venomous riposte for Fulham, may have been momentarily disappointed to see the champions snatch victory from their grasp.
If so, both team and supporters quickly recaptured the party mood. Remembering that the result did not really matter, they stayed long after the final whistle to rejoice in Walsall's extraordinary achievement.
For until the pounds 30,000 signing Richard Green appeared as a substitute in the last minute, not one of the home line-up had cost a transfer fee. Ray Graydon, their 51-year-old "rookie" manager, has taken a team who finished only four points clear of relegation last May and transformed them into worthy runners-up.
In contrast, Kevin Keegan has spent pounds 12m rebuilding at Craven Cottage. Yet there was seldom much between the teams. Fulham enjoyed the greater share of possession and created the clearer chances, but Walsall's spirit and organisation more than compensated for any disparity in quality.
Barry Hayles, one of two pounds 2m players in the visitors' ranks, caused Walsall particular problems with his speed and strength. Fortunately for Walker, Hayles' co-striker, Dirk Lehmann, put two good opportunities over the bar early on.
Walsall took the lead in the 40th minute, turning deep defence into rapid counter-attack after clearing a corner. The Croatian Darko Mavrak sent Steiner, a Swede on loan from Bradford, through to shoot against the post. Steiner kept his composure to stroke in the rebound.
Fulham drew level in first-half stoppage time. Chris Coleman's stunning crossfield pass picked out Smith, himself on loan from Crystal Palace. The wing-back's diagonal shot tore past Walker in a blur.
The second Walsall goal, like the first, arrived just as they were struggling to contain Fulham. Dean Keates' 70th-minute free-kick was headed back across the six-yard area by Adrian Viveash and Roper pounced from four yards.
"It's great pitting your wits against the England coach, the people's favourite," said Graydon. Keegan saw no reason for either to fear the First Division. Having promised to give any divisional manager's award to Graydon, he now went a step further. "If Ray gets the Manager of the Year, he deserves it. I think it's the achievement of the season - in any League."
Walsall (4-4-2): Walker; Marsh, Roper, Viveash, Pointon; Wrack (Carter, 78), Larusson, Keates, Mavrak (Green, 90); Steiner (Eyjolfsson, 74), Rammell.
Fulham (3-5-2): Taylor; Symons, McAnestie, Coleman; J Smith, Collins (Moody, 80), Hayward, Trollope (Bracewell, 44), Brevett; Hayles, Lehmann (N Smith, 80).
Referee: J Kirkby (Sheffield).