Karim Benzema seemed to have opened the Madrid floodgates on Saturday after 19 minutes but unheralded Granada shockingly struck back just three minutes later thanks to Mikel Rico.
However, normal service was soon resumed for Jose Mourinho's side as goals from Higuain, Benzema, Sergio Ramos and Cristiano Ronaldo ensured that Los Blancos maintained a six point lead over second placed Barcelona.
Speaking to Real Madrid's official website in his post match press conference, Karanka said, "It's not the norm that Higuain and Benzema play together, but they can."
"They did so in the second half of our previous match and they were both starters tonight."
"The team is more together and balanced when it works hard and covers a lot of ground. Both strikers are very dangerous up front."
Karanka also delved into Benzema's potential injury setback that forced him off the pitch.
"Benzema's injury doesn't seem serious at first. It happened during the first half; he strained himself and we took him off as a precaution," he added.
The former Madrid defender also highlighted that his side's third strike gave them some much needed breathing space.
"Our third goal was crucial; we became more dangerous in wider spaces after it. Higuain and Benzema again proved they can play together," Karanka explained.
"We knew Granada would defend fiercely and they were organised in the first half. It was difficult for us to attack. Granada are built to defend and counterattack."
"Every half-time chat is different. They are conditioned by your opponent and the competition. It isn't the same to concede a goal in the Copa del Rey and in the league."
"That's what half-times are for. You use them to talk about mistakes and correct them."
Karanka sought to play down the seemingly frustrating celebration by club talisman Ronaldo after the Portuguese grabbed his side's fifth goal of the night.
"A player of Cristiano's professional nature and experience gets angry when things don't turn out," he added.
"We all know how much he wants to help the team. The gesture he had after scoring was just a sign of rage, that's all."
"(Alvaro) Arbeloa missed the match because, after talking to him, we decided he wasn't fully fit to play. There were other players in better shape and we must have the best readily available."
"Granada's supporters set an example for everyone. They came all the way to cheer their team on and should be praised for it."
Lastly, Mourinho's right hand man also revealed why the Special One himself was not in attendance at his side's customary post match briefing to reporters.
"Jose Mourinho had to leave due to a family problem and I've explained in the past why I sometimes speak in his place. Today [Saturday] it was for a different reason," Karanka concluded.
Right-back Sergio Ramos, who marked his return from a long injury layoff to find the net against Granada insisted that his side fully deserved their eventual 5-1 win.
"Maybe they are a very good team, as they made life complicated for us, but in the second half we did better and had more chances," said Ramos.
"We were worthy of the victory, we had the ball almost all the time, but [in hindsight] I prefer our second half display."