Two first-half penalties from Michael O'Connor and Anthony Elding dumped out the team that saw off the likes of Chelsea and Liverpool in last season's FA Cup.
Crewe were handed the perfect start after 14 minutes when Darren Moore brought down Tom Pope in the box.
After a heated argument with new striker Elding for the right to take the spot-kick, O'Connor drilled the ball home with aplomb.
Minutes later, Diego Leon almost pulled the Tykes level, but keeper Steve Collis managed to tip his free-kick onto the crossbar.
Leon came close again on the half-hour mark. Martin Devaney whipped in a wicked cross and the winger cracked a low volley inches wide of the goal.
But the Railwaymen were handed another penalty in the 36th minute as this time Byron Moore was brought down by Robert Kozluk.
Elding stepped up this time and made no mistake with a high shot that left Luke Steele with no chance.
Devaney cut inside Billy Jones but was denied by Collis and Dennis Souza headed over as the Tykes tried to get back into the game.
Some superb last-ditch defending denied Leon again after the break, before Collis dived low to keep out his follow-up shot.
Davey threw on John Macken to try and get Barnsley firing but the striker fired a great chance from ten yards high over the bar.