Relegated Dunfermline looked like doubling their tally of home wins after repelling some early second-half pressure after Paul Willis had given them a 20th-minute lead.
But Liam Kelly fired an equaliser with four minutes left and 19-year-old substitute Winchester capped his second appearance with a cool finish in the 89th minute.
Dunfermline made seven changes following the 4-0 defeat by Dunfermline that sent them down. Bernando Fernandez made his debut in goal while the likes of Willis, Ryan Thomson and Steven McDougall made rare starts.
Kilmarnock also gave rare starts to goalkeeper Kyle Letheren and Ross Barbour.
Kilmarnock failed to capitalise on their early pressure and Willis gave the home side the lead.
Joe Cardle's free-kick was headed back across goal by Liam Buchanan and was tapped home from close range by the midfielder.
McDougall shot wide from a half chance and Willis almost returned the favour for Buchanan but Michael Nelson cleared.
Jordan McMillan's persistence earned Buchanan a shooting chance but Ryan O'Leary dived in to block.
Kelly got Killie's first effort on target just before half-time but Fernandez was comfortably behind the midfielder's bouncing long-range strike.
Kilmarnock created a series of chances just after the break.
Fernandez stopped a William Gros shot with his foot and James Fowler mis-hit the rebound.
Barbour then sent a free header wide from 10 yards following a Dean Shiels free-kick.
Andy Dowie then headed off the line under pressure from Gros after Harkins had lobbed the ball over the head of Fernandez.
The Spaniard spilled Harkins' drive but caught the ball at the second attempt and Shiels volleyed wide after Gros' flick.
Killie sent on Winchester for Barbour and Gros had their next effort, flicking a header wide.
Dunfermline survived a dangerous ball across goal from Lewis Toshney and Kelly blasted over after a short corner.
Killie brought on teenager Chris Johnston while Dunfermline added experience to their ranks with the introduction of David Graham, Martin Hardie and Andy Kirk.
The hosts were looking far more comfortable and Willis earned himself a chance for a second when he flicked the ball inside Ben Gordon and attempted to lob Letheren but the Kilmarnock goalkeeper stood up well to catch.
Dunfermline looked like holding out for a second successive home win but Kelly struck a 20-yard effort into the top corner after a Shiels shot had been closed down.
Dunfermline had the ball in the net within seconds but the goal was ruled out.
Kirk's header from a Graham cross looked to be going in and Hardie was flagged offside as he helped the ball home on the line.
Dunfermline were made to pay when right-back Toshney overlapped and sent a square ball across for Winchester to stroke home from six yards.
Elsewhere, Darren Mackie failed to end his Aberdeen career on a high as the Dons drew 0-0 at home to St Mirren, while a much-changed Hibernian side lost 2-0 at Inverness Caledonian Thistle ahead of the Scottish Cup final.