Burnley had beaten Morecambe, Salford City, Oldham Athletic and Lancashire rivals Blackpool heading into the behind-closed-doors friendly in Birkenhead.
But they were made to come from behind on this occasion to ensure their 100 percent record ahead of the 2021-22 campaign remained intact.
The Clarets could have taken the lead as early as the fourth minute when Rovers keeper Joe Murphy did well to palm Ashley Barnes's header around the post from Ashley Westwood's delivery.
McNeil wasn't far away from breaking the deadlock as the quarter-of-an-hour mark hit when sending his set-piece inches wide of the upright.
The Young Lion turned provider 12 minutes later when crossing for Jay Rodriguez, who was off-target with his header.
The hosts had the ball in the net against the run of play when Mani Dieseruvwe followed up Callum McManaman's effort, but their celebrations were short-lived as the linesman's flag signalled offside.
Johann Berg Gudmundsson almost capitalised on a good opening at the other end just minutes later, only for Murphy to turn his attempt for a corner.
Burnley enjoyed the better of the first half, but it was Micky Mellon's men that took the lead just before the hour.
Substitute Nat Knight-Percival connected with a corner and his header beat Clarets goalkeeper Wayne Hennessey.
Sean Dyche's side were facing their first defeat of pre-season squarely in the face.
However, they took a step towards preserving their unbeaten record when equalising with 20 minutes remaining. Matt Lowton supplied the cross and Barnes headed beyond Murphy to make it 1-1.
The visitors almost went ahead shortly after when efforts from Lowton and substitute Matej Vydra both hit the woodwork.
The full-back's shot flicked the top of the crossbar in the 73rd minute before the Czech Republic international curled an effort on to the post after linking up with McNeil.
The game was heading for a draw, until McNeil intervened with his first finish of pre-season.
The winger smashed the ball home from outside the penalty area to secure a 2-1 victory for the away side.