Die Schwarzgelben's patience was ultimately rewarded as they climbed above Bayer Leverkusen and into second place in the Bundelisga thanks to three second-half goals
Die Schwarzgelben initially struggled to break the visitors down but made the crucial breakthrough six minutes after the interval when defender Mats Hummels tapped home a rebound.
Robert Lewandowski doubled the hosts' advantage soon after and Henrikh Mkhitaryan put the seal on a win that propelled Dortmund into second place in the Bundesliga standings, two points ahead of Bayer Leverkusen, who suffered a shock defeat at home to Mainz.
"It was a tough job," Klopp told reporters after the game. "Nurnberg were very good in tight spaces but we defended very well.
"We knew at the break that if we continued as we were playing that we would be successful."
Mkhitaryan, meanwhile, was just as delighted that Dortmund had managed to put last weekend's surprising Bundesliga loss at Hamburg firmly behind them by following up their midweek Champions League win at Zenit with another victory.
"Today, we did everything to get the three points," the Armenia international enthused.
"The match against Hamburg was not in our minds. For us, we always only count the last and the next game. In the end, we won today [Saturday] and it was very well deserved.
"We now need to win as many [games] as possible to keep the second place. The season is still long and it will be a hard road."
Dortmund will be hoping to solidify their grip on second spot when they travel to Freiburg next weekend.