Fleetwood Town defender Cian Bolger had netted at both ends before the Liverpool loanee struck to put the Glovers ahead.
The right-back hit an excellent first-time swerving volley into the bottom corner for the first professional goal of his career.
Jordy Hiwula looked to have forced the tie into a penalty shootout late on but a last-gasp Francois Zoko effort saw Yeovil progress to the last four.
Whelan picked up the man of the match award on just his second start for the club and believes he has firmly grasped his opportunity to impress boss Darren Way.
“It’s always nice to add to your goal tally,” he told iFollow Glovers.
“(Alex) Fisher’s taken a touch in the box, set it back and I thought because of the pitch and the conditions instead of taking a touch, and maybe it bobbling off me, I’d hit it first time. I swung my left foot at it and it’s ended up in the bottom corner luckily for me!
“I’ve had to stay patient because the lads have been excellent. I’ve stayed eager, stayed hungry and I think I’ve taken my chance.
“It’s a great feeling to keep the Wembley dream alive and I was happy to contribute to that.”
The victory was Town’s third in a row in all competitions and sees them just 90 minutes away from a final at Wembley.
Whelan feels the squad’s task now is to carry on their impressive recent form.
He said: “When you go up against a League One side you’ve got to fight and stay together and that’s what we did.
“We’ve done well in the league of late and now we’re 90 minutes from Wembley so everything is coming together. We’ve just got to keep the form going.”