Winchester curled a glorious left-footed strike into the top corner to put his side ahead with four minutes left at Easter Road.
But Hibs then equalised for the second time in three minutes when Leigh Griffiths scrambled home from close range to deny Winchester the prolonged joy of scoring a winner in the Clydesdale Bank Premier League contest.
Now the Northern Irishman aims to go one better when the teams meet again at Rugby Park on Sunday in the William Hill Scottish Cup quarter-finals.
The 19-year-old said: "We had to win the game to keep us in the top six so we wanted to win it.
"After they scored we knew what we had to do and getting the goal was brilliant, it was just conceding the goal two minutes later that killed us. We were disappointed and we will be looking to go further in the cup but it will be hard because both teams want to progress. But we will have the faith and hopefully we will get the win."
The youngster is hoping to emulate the cup heroics of last season which saw Kenny Shiels' men triumph over Celtic at Hampden to claim Scottish Communities League Cup glory.
Winchester savoured the atmosphere around the club and hopes to play a more direct part in another triumph.
"We won the cup last year and we know what it felt like and we want to get that same feeling this year, so hopefully we do well on Sunday and we can get the win," he said.
"I wasn't part of the squad but the lads that won it were unbelievable."
- Sports & Recreation
- Leigh Griffiths