Robbie Blake missed from the penalty spot as Doncaster crashed out of their second cup competition in the space of four days, losing 5-3 following a 1-1 draw.
Chris Brown's last-gasp goal cancelled out Mathias Pogba's first-half strike to take 10-man Crewe to penalties.
But Blake smacked the crossbar with his spot-kick as the Alex held their nerve and tucked away every penalty.
A bug forced Rovers boss Dean Saunders to make five changes to the team that lost to Oldham in Saturday's FA Cup clash.
But the Welshman would have been pleased with his team's bright start as Alex full-back Gregor Robertson produced a vital block to deny Brown before Blake hit the foot of a post with a fierce 30-yard free-kick.
Crewe took control and Chuks Aneke saw a header palmed onto the crossbar by Gary Woods while Bradden Inman was denied by two great saves from the goalkeeper.
The Railwayman broke the deadlock on the stroke of half-time when Max Clayton cut back to give Pogba the simplest of finishes.
The visitors should have levelled when James Husband flashed an inviting ball across the face of goal but Steve Phillips kept out Brown's close-range shot with his feet.
Pogba hit the upright with a header from Inman's centre before Crewe's Matt Tootle saw red for his second bookable offence in injury time.
Brown then bundled the ball in at the far post at the death but the game still ended in heartbreak for Rovers.