Norwich manager Daniel Farke has urged his players to "stay focused" as they close in on a return to the Premier League.
The 1-0 victory at Derby means they need two points to seal promotion after one season out of the top flight.
Norwich dominated the first half and should have made more of their control but still looked comfortable after Kieran Dowell's free-kick put them ahead.
Dowell had already served notice of his quality from dead balls by finding the side-netting but when he was fouled just outside the box in the 21st minute, he whipped the free-kick into the top-left corner.
Norwich's quick movement threatened to overwhelm Derby but the closest they came to a second was when Todd Cantwell had a low shot saved.
Derby came out with more purpose in the second half and a long ball put Colin Kazim-Richards in at the back post in the 53rd minute but Tim Krul saved at his near post and did even better a minute later to turn away a Teden Mengi drive.
Krul denied Patrick Roberts in the 74th minute after the winger beat three defenders, although he almost cost his side two points in stoppage time when he was robbed by Kazim-Richards but Graeme Shinnie fired over.
Farke said: "I'm a happy man if I'm honest because the other results show it's not over and you have to keep going and you always have to be switched on.
"It was a hard-fought win, not a magic night like Tuesday (a 7-0 win over Huddersfield) but if you are working a little bit longer in football that's exactly what you expect.
"We got so much praise, so many compliments and then we have to deliver four days later in a difficult away game against a side fighting to stay in this league.
"In the past 90 points was always enough so my gut feeling was this win was really important.
"The pressure is now off a little bit and my feeling right now is I'm pretty sure at the end of the season we will definitely celebrate promotion.
"But it's not over the line and Brentford and Swansea have proved they are capable of winning all of their games so we have to stay focused.
"That's the only danger, we have to take care that we perform with the same concentration and then I'm quite confident we will bring it over the line."
Derby manager Wayne Rooney felt his side deserved a point.
He said: "I thought we performed very well, especially second half, and we can take some encouragement from the performance.
"For the first 25 minutes we showed Norwich too much respect and I felt after that you could feel the lads growing in confidence.
"Second half we got at them and caused them problems and overall I thought the performance was good and we deserved at least a point.
"We move on, the next couple of games are big for us, we need to take points leading into Birmingham at Pride Park so the next few games are huge for us.
"The performances in the last two games have been good but now we have to focus on getting wins because we're at a crucial time of the season."