Former Port Vale striker Billy Paynter's double completed a quick-fire comeback for Doncaster, who stay two points ahead at top of the table.
Max Clayton had fired Crewe ahead, but Paynter came off the bench and netted twice in four minutes to ensure Rovers stayed in pole position.
Oliver Turton blew a late chance to earn the Alex a draw they arguably deserved as Crewe suffered their second defeat in a week since lifting the Johnstone's Paint Trophy.
Flynn said: "Once again we have bounced back from defeat and it could prove a pivotal result.
"It was probably our least effective performance for about three months.
"The second half was littered with mistakes, but what we showed was desire and a willingness to get back into the game and that has become a characteristic of this team.
"Billy was excellent, always gets chances and he took them with aplomb. We have five strikers vying for the same position so you want to make an impact when you get your chance and that is exactly what he's done.
"We are excited now, but we can't ask favours from anyone else. If we take maximum points from the last few games we get promoted."