Tottenham looked set to fail their first test without the injured Harry Kane as his deputy Fernando Llorente made an unwanted impact at the other end with an own goal to hand Fulham an early lead.
Dele Alli levelled six minutes into the second-half, but later hobbled off having appeared to pull his hamstring in another devastating injury blow to Spurs’ challenge on four fronts.
However, after Winks burst into the box to meet substitute Georges-Kevin N’Koudou’s cross with virtually the last touch of the game, Spurs tightened their grip on third. They have the cushion of a seven-point advantage over fifth-placed Arsenal and Manchester United in the race for a top-four finish.
Fulham on the other hand are seven points off safety and look set to return to the Championship after just one season back in the top flight.
After splashing over £100 million in transfer fees to little success in the summer, Fulham added Dutch international Ryan Babel till to the end of the season from Besiktas on Tuesday.
The former Liverpool winger’s pace and strength made an instant impact against an unsettled Spurs defence as Pochettino switched to a back three.
Babel brushed aside Davinson Sanchez for the first big chance of a bitterly cold afternoon by the Thames, but Hugo Lloris made the first of a series of fine saves to bail out the visitors.
Fulham’s bright start was rewarded 17 minutes in, courtesy of a stray Tottenham leg, as Llorente, starting for the first time in the league this season in Kane’s absence, miscued a Jean Michael Serri corner into his own net.
Spurs dominated possession, but shorn of Kane and Son Heung-min in attack were going largely nowhere with it and Fulham will live to regret not making more of chances to extend a slender lead before the break.
Babel headed over from close range before Lloris produced an incredible stop to parry Andre Schurrle’s volley.
Aleksandar Mitrovic headed home the rebound, but the offside flag was raised against the Serbian striker.
As so often this season, those wasted opportunities allied to some slack defending cost Claudio Ranieri’s men.
Spurs were level soon after the break as Christian Eriksen’s dinked cross to the back post picked out Alli to power home a header.
With Fulham no longer able to sit back and counter, the game swung from end to end. Lloris again did well to clear a dangerous through ball ahead of Mitrovic, while a desperate block from Maxime Le Marchand denied Eriksen.
Spurs enjoyed more control of the final quarter and came close when left-back Danny Rose cut inside and saw his shot crash against the crossbar via a deflection off Denis Odoi.
A devastated Alli then limped off to make way for N’Koudou and looks certain to at least miss Thursday’s League Cup semi-final, second leg away to Chelsea.
However, the French substitute was to have a telling impact when his wicked swinging cross was met by Winks’ run and header at the back post.
Download our app and read this and other great stories on the move. Available for Android and iOS.