An early goal for Josh Parsons was chalked off for offside but the Racers did take the lead on ten minutes when Parsons took advantage of Elliot Coopers fumble in the Alsager goal after a James Hancocks cross.
Alsager soon returned the scores to level though when a Ben Glendon free-kick was left by the Racring defence and Jahmari Hyatt headed home from four yards.
Warwick needed to improve in the second half and they did. Parsons fired just over from 35 yards before he cleverly chipped the ball in for Chris Mayuba to clip the ball over Cooper to retake the lead on 64 minutes.
Hancocks fired just over before a super through ball from Hanni Salami saw Dylan Parker finish off Alsager with a fine finish.
Racing will now play another step six side in Dunkirk FC in the next round.