Clarets boss Dyche has been named Manager of the Month after guiding his side to automatic promotion to the Premier League.
Meanwhile, Benin international forward Gestede hit six goals in six starts as Rovers mounted a late play-off push.
In Sky Bet League 1, Darren Ferguson claimed the manager's prize after an excellent run of form secured a play-off berth for Peterborough.
Rotherham are also heading into the post-season with hopes of promotion and their striker Kieran Agard picks up April's player gong in the division.
Newly-appointed Portsmouth manager Andy Awford is last month's best boss in Sky Bet League 2, with Fleetwood Town's on-loan midfielder Josh Morris taking the player honours.
Former Sheffield United and Nottingham Forest boss Dave Bassett is the chair of the Sky Bet Manager of the Month judging panel, and has paid tribute to Dyche for his achievements this season.
The 42-year-old gained 13 points from six games to engineer a top-flight return.
Bassett said: "Sean had to cope with injuries to key players during the month and the pressure of sustaining a remarkable push for promotion. He kept the momentum going in a series of closely contested matches throughout the month."
Sky Sports' Football League pundit Don Goodman added: "Sean is one of the managerial success stories of the season.
"He has got the best out of every player as an individual and moulded the group of players into a team with real spirit and lots of quality.
"Allied to that, he's got his tactics spot on most of the time and that's all a recipe that brings success."
Gestede's goal haul for Blackburn during April included a hat-trick of headers in the 4-2 win at Birmingham, and Rovers manager Gary Bowyer admits the striker has been a "fantastic signing".
"As a person, he is top class," explained Bowyer. "He has played a massive part for the team with some very impressive performances. His goals have been the icing on the cake.
"He works hard to improve his game - and he is only going to get better."
Fillip for Ferguson
Ferguson guided Peterborough to Johnstone's Paint Trophy glory at Wembley at the end of March, and Posh continued in that rich vein with five wins from seven League 1 games.
Bassett said: "Darren maintained very positive play during the month, especially when it became clear that the last play-off place was within their grasp. It's another exciting end to the season for Posh fans."
Meanwhile, after being used in a wide role, Agard began operating more centrally for Rotherham in April - and weighed in with five goals in six games.
Millers manager Steve Evans said: "This is just what the lad deserves. He's got 25 goals this season.
"Kieran has a great enthusiasm for the game. He's a very honest hard-working guy and one who is enjoying his football at the moment."
Awesome from Awford
Having initially been put in caretaker charge, Awford oversaw a 13-point haul from 15 available in an April full of attacking intent, taking Pompey from the brink of relegation to the comfort of mid-table in League 2.
Goodman said: "No one envied Andy when he took on the massive challenge at Portsmouth.
"He has not only halted the free-fall. He has made the club safe. And now they're a club looking up again."
Up at Fleetwood, tireless displays from Morris and two fine goals helped clinch Town a play-off place.
Fleetwood manager Graham Alexander said: "Josh has great ability on the ball, he has great awareness about the game of football and he is a very good young professional footballer.
"We are really pleased to have him here and we thank Blackburn Rovers for that."