Elisha Sam put the Magpies in the lead before half-time but Maguire headed an equaliser on the hour and then added another goal with just four minutes left.
Asante grabbed a third from the spot after Liam Mandeville was fouled.
Here are Liam Norcliffe’s Chesterfield player ratings from the match...
Scott Loach 7
Nothing he could do about Sam’s excellent opener. He made a fantastic reaction save late on to keep out Cameron’s close-range header which would have made for a nervy ending.
Jeff King 7
His mistake led to Notts’ opener but he redeemed himself after the break with a great dinked cross for Maguire’s equaliser and claimed a second assist, again for Maguire.
Jamie Grimes 8
Solid display. Almost grabbed an equaliser before half-time but goalkeeper Vitezslav Jaros denied him at the near post. Made a crucial block to deny Rodrigues with the score level at 1-1. He was assured throughout.
Laurence Maguire 9
Man of the match. Two goals and a brilliant performance overall. Hardly put a foot wrong and led by example.
Alex Whittle N/A
Sadly he was forced off injured in the first-half with a slight groin strain but it is not thought to be serious.
Jim Kellermann 8
A really good all-round performance in the middle of the park. Kept possession well, snapped into tackles and had shots at goal. Back to his best after his goal against Yeovil.
Tom Whelan 7
Struggled to have an influence in the first-half but got on the ball after the break and showed his class. Never stopped scrapping away and a lot of good things Town did went though him in the second-half.
Liam Mandeville 7
Not in the game at all in the opening 45 but came to life in the second-half and helped swing the game in Town’s favour. He started running at the Notts defenders and delivered some dangerous crosses. His run and trickery won the penalty for the third goal.
Saidou Khan 8
Came into the starting line-up and showed Paul Cook exactly what he is all about. He dribbled, pressed, passed, attacked and didn’t shirk his defensive work. Another one who put in a top all-round performance.
Calvin Miller 7
Final product let him down at times but he kept on working. Had to adapt when he was moved to left-back following Whittle’s injury and he deserves credit for that. Worked tirelessly and put in a shift.
Akwasi Asante 7
His hold-up play was not as sharp as usual but he was tasked with occupying the County defence on his own at times and he was crowded out. Perhaps he is feeling the effects of the busy schedule. But he kept on plugging and tucked away the penalty for the third goal.
Joe Quigley 4
Came on for the injured Whittle in the first-half but was subbed off midway through the second period. His hold-up play and touch was lacking and nothing was sticking.
Joe Rowley 7
He was lively when he came on down the left and played his part in the win with some direct dribbling.