The starlet was introduced late in a game his teammates were dominant in and picked up a big win with goals in either half
Onyango replaced Andre Gomes in the 85th minute as he enjoyed a full debut for the Everton senior side.
Dominic Calvert-Lewin, Richarlison and Yerry Mina scored the three goals for the Toffees to progress at the expense of the struggling Championship side.
The win ensured the Merseyside club reached the fifth round of the FA Cup for the first time since they did so in the 2015/16 season. They have also progressed from 12 of their last 13 FA Cup ties against teams from the lower leagues.
Coach Carlo Ancelloti also gave a debut to Thierry Small, 16, with five minutes remaining and he became Everton’s youngest-ever player.
The progress delighted Everton’s assistant Duncan Ferguson, who stated his side deserved the win for they were dominant
“I am absolutely delighted – we played very well and took the chance. We were dominant,” Ferguson said as was quoted by BBC Sport.
“We hit the bar, had a goal disallowed and in the second half we pushed on. It was a good all-round performance.
“We were dominant right through, we were the better team from the go. We are in it to win it.”
Although he did not talk about Onyango, Ferguson said Small was brilliant and cool: “Brilliant, great for him, I’m made up for him, really delighted,” he added.
“He was cool and we are delighted for him. Sixteen-years-old, [it’s] unbelievable and hopefully [this appearance] will be the first of many.”
On his part, Sheffield Wednesday’s Neil Thompson picked out some positives from the match despite failing to score even one goal.
“We did well first half and were good on the counter. We used the ball well but we needed to penetrate more,” Thompson said.
“They got two goals from set plays which is disappointing but we gave a good account of ourselves. It gave us a chance to pit our wits against some of the best in the country.
“We still have people missing and we have a duty of care to make sure everyone is right.”
Onyango has now joined Barnsley’s Clarke Oduor in the next phase of the competition.