Fourth-place City is six points behind league leader Arsenal and only off the pace because of its dire away record. United is a point back in sixth after seeing its run of three wins in a row end at a ground where City has already lost this season.
City remains many pundits' title favorite despite its sketchy start where the team has been flawless at home but picked up just four points from a possible 18 on its travels.
Crushing a supposed title rival in such a devastating manner sends out a clear message, especially since Spurs had only conceded six goals in 11 games before Sunday.
City was 5-0 ahead after just 56 minutes, with Navas starting the rout after just 14 seconds for the fifth quickest Premier League goal. Aguero netted in each half to add to an own goal by Sandro and a brilliant strike by Alvaro Negredo, leaving Navas to complete Spurs' humiliation in injury time.
"We have to be ashamed of a result like this," said Tottenham manager Andre Villas-Boas, whose team is ninth despite spending more than 100 million pounds (now $160 million) on mostly attacking talent in the summer.
Not since a 7-1 loss to Newcastle in December 1996 have they been beaten by a six-goal margin and it could have been a lot worse. Such was City's intensity in the opening minutes that Spurs midfielder Sandro vomited on the pitch.
Now City has to turn around its away form.
"This team at home score more than four goals a game," Pellegrini said. "The problem is away . but for different reasons we have not had the results we wanted.
"I am absolutely sure if we continue to play like this we will get results away from home."
Spurs goalkeeper Hugo Lloris was making his first league start since taking time off to recover from the effects of concussion, and was at fault for City's first two goals because of weak clearances.
United was looking to climb into the top four for the first time since August but could have been playing with 10 men for most of the game at Cardiff after Rooney hacked at the calf of Jordon Mutch as they chased down a ball on the left wing in the eighth minute.
Rooney received only a yellow card and scored seven minutes later when his deflected shot looped into the corner.
Fraizer Campbell equalized but Evra's header on the stroke of halftime looked like earning United victory until Kim's intervention in the second minute of stoppage time.
"I'm disappointed we didn't take three points," Moyes said. "Cardiff made a game of it and put us under pressure. We gave away a silly free kick which led to their second goal and didn't defend it well enough."
