Cobblers forward Vadaine Oliver went closest to a breakthrough in the first half, striking the crossbar from close range.
Curtis Davies headed wide in the second half for the visitors, who failed to register a shot on target.
Northampton manager Keith Curle had hoped Wayne Rooney would be rested for Friday’s tie, but the former England captain was one of three survivors from the Rams side that beat Hull in the Championship last weekend.
Rooney and his team-mates were firmly on the back foot in the opening exchanges, however, with Cobblers centre-forward Oliver proving a constant thorn in the Derby defence.
The striker scooped the ball on to the top of the crossbar from point-blank range after County had failed to clear Jordan Turnbull’s effort, before sending a towering header narrowly wide from Paul Anderson’s deep cross.
Derby had created little up to that point, but they were adamant Northampton should have been reduced to 10 men when the otherwise impressive Charlie Goode hauled Jack Marriott to the ground with the Rams striker through on goal.
The visitors appealed for a red card, but their protests were waved away by referee Darren England, who didn’t award a free-kick.
Phillip Cocu’s team offered more of a threat in the second half and went close to an opener when Curtis Davies sent a powerful header past the post from Marriott’s teasing delivery.
Town midfielder Chris Lines hooked a volley over the crossbar late on, but neither side could muster a winner.
Northampton manager Keith Curle, speaking to BBC Sport: “We all needed to be on the same page. Today showed the work in progress and the work we put in at the football club.
“We’ve earned the draw over 94, 95 minutes. The replay gives us another opportunity, to go to Derby and put in another performance that we’re proud of. We might be able to express ourselves a little more on the ball at their place.”
On Charlie Goode’s foul on Jack Marriott: “I did see it. The referee was unsighted. A red card would have changed the flow of the game massively, but we showed that we can compete against a very good football club.”
Derby manager Phillip Cocu, speaking to BBC Sport about Goode’s foul: “If he doesn’t pull Jack Marriott down, Marriott would be one-on-one and probably score.
“There’s only one decision to make. I cannot imagine why he doesn’t give it. The referee tried to be man of the match and he became man of the match.
“Northampton deserved credit. They played a good game. They had passionate home fans, it was a great atmosphere. They played a direct style of football.”
C: BBC Sport