The Rams fired themselves to within two points of second-placed Bolton Wanderers with a fifth straight away win.
Nathaniel Mendez-Laing and James Collins did the majority of the damage in the first half at Highbury.
Jayden Stockley pulled one back but Tom Barkhuizen sealed a vital three points in County’s promotion push in stoppage time.
A delighted Warne said: “We did enough to win and, come the end of the season, it doesn’t matter how you win, it’s just important that you win.
“We’ve done well away from home in different football matches. At Oxford and Wigan, they were different matches to today. It’s a boost for us. They’re good lads and they want to get near the summit.
“There aren’t many weekends when you know you’re going to have a positive trajectory with a win because of the FA Cup.
“To take ourselves into third is great. I think we’ve got another gear.
“Over the course of the season you can
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