The 26-year-old striker was handed his first Bluebirds start in 11 months at the Crown Ground and broke the deadlock just after the hour mark with a sublime strike as he flicked the ball over a defender's head before rolling his effort into the left corner.
Strike partner Rudy Gestede added a second barely a minute later to ensure the 2012 finalists set up a meeting with Maynard's former employees West Ham in the third round.
It has not been easy for Maynard since he swapped Upton Park for the Cardiff City Stadium and he was largely a frustrated spectator during their march to the Championship title last term after damaging knee ligaments.
But now, back to full fitness and part of a Premier League squad, Maynard is keen to make up for lost time.
"I was out for eight months last season and I've had a decent pre-season and been looked after well," said Maynard.
"I've not been able to go gung-ho because I still need to manage my knee but I feel fit, I feel sharp and I'm just hungry to get as many minutes as possible.
"Whenever I play I always expect to be scoring or getting chances. Thankfully I got a run-out and showed I can still score goals."
Mackay is likely to recall Fraizer Campbell for Saturday's match against Everton after his two goals earned the win over Manchester City on Sunday, the Bluebirds' first victory in the top flight for over half a century.
Maynard added: "It's a disappointment that I've not played as many minutes as I would have liked but it's a squad game.
"We had a fantastic result on Sunday and I was as chomping at the bit to get a run-out but hopefully I can give the gaffer some food for thought and whenever I get the chance I'm looking to take it.
"I'd like to think me and Fraizer have been taking that chance and obviously it's given the gaffer a few headaches which he'd probably like."
Mackay's side were made to work hard for their 2-0 victory in Lancashire against a team currently propping up the Football League.
Yet the Scot saw enough of James Beattie's men to claim they will soon be making an ascent of the League Two ladder.
Mackay said: "You look at teams and you say, 'Are they playing for the manager? Are they working hard or are they going through the motions?'.
"Accrington absolutely applied themselves for their manager. They worked hard, ran hard and I don't think it'll be long before they're off the foot of the table."