Derby closed to within two points of second-placed Bolton and four of League One leaders Portsmouth with a 3-1 win over Fleetwood on Saturday.
After the Cod Army missed a handful of early chances in Charlie Adam's first home game in charge, Nathaniel Mendez-Laing struck a clinical opener just before the half-hour to put Paul Warne's side in front.
The in-form James Collins connected with a corner from the right to glance a second - and his 16th of the season - on the stroke of half-time.
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The Rams were shot-shy for much of the second half, which set up a tense finale once Jayden Stockley had headed home a cross from Shaun Rooney,
But Tom Barkhuizen finished the job late on after an excellent run by Max Bird to secure a fifth-straight away win for the visitors.
While Derby climb as a result of their ninth win in their last 11 league games, Fleetwood stay rooted to the bottom of the table, five points from safety.
Watch each of the four goals...
The managers
Fleetwood's Charlie Adam:
"I couldn't be any more proud of these lads. Again, we're disappointed with the goals that we lost. But we'll take positives from the performance, the endeavour, the shape and the organisation. They took everything in. They came up against a quality side in Derby, they punished us. But I couldn't be prouder of these players.
"This group of players are taking on what we're trying to give them as a staff. If they keep giving me that then we'll be pushing up the league there's no doubt about that. My two midfielders were magnificent. I said that to them in the dressing room, they're playing against a Premier League player in Conor Hourihane and I thought they were magnificent against him.
"If they get that level of intensity and quality during games then we're a good side and I'm looking forward to the rest of the season with them. We could have nicked a point. We had chances. But it comes back to moments in games. We conceded a set piece in the second minute of added time in the first half and then we're 2-0 down.
"If you don't take your chances with the quality that Derby have you can get punished. But I want to take the positives and we'll build on that for next week."
Derby's Paul Warne:
"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 from 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.
"In fairness, at 2-1 I can't say my blood pressure wasn't through the roof because it was. Every time they went forward you're always thinking the worst so to get the third goal was a relief. Over the course of the season you can outplay teams at Pride Park, but away from home these games are difficult. It's winter football.
"We could have been better, but I'll take three points over a better performance and a draw. We need to be better and have more control in games. I thought we overcomplicated it a bit in the second half. Our own errors allowed them back into the game and that's disappointing. We allowed the opposition in and then had to weather the storm."
What's next?
Derby are back in action at 7pm on Tuesday January 9, when they face Bradford in the last-16 of the Bristol Street Motors Trophy.
Fleetwood return at 3pm on Saturday January 13, when they travel to face Cambridge at the Abbey Stadium in Sky Bet League Two.