Shaun Harrad scored the only goal of the game from the penalty spot in the 15th minute. The decision came after winger Marc Goodfellow was bought down in the area.
Rams goalkeeper Saul Deeney had his work cut out for most of match and just 10 minutes after the penalty he saved superbly with his legs to deny Harrad a second goal.
Albion substitute Russel Penn came close to scoring in the second half, but Deeney made another smart save.
Goodfellow had chances to double the lead, but it was a wide volley from Richard Walker on the hour-mark that could have put Albion 2-0 ahead.