Dyer converted a clinical breakaway goal 17 minutes from time, ramming home a cross by Tom Cleverley as the Cobblers lost their second consecutive match 2-1 after nosing ahead.
Alternately, it was no more than the visitors deserved as their class eventually told, although the Cobblers were committed throughout and could have salvaged a point in injury time when Billy Clarke's shot was saved by David Martin and Jason Crowe's follow up was blocked on the near post.
The home side went ahead in bizarre fashion after 15 minutes when a corner by Danny Jackman saw Crowe's header blocked on the line.
Leon Constantine then had a goalbound effort saved but, when Matt Oakley hacked at a clearance, it bounced off the body of Kerrea Gilbert and flew back into the net.
Leicester were handed a lifeline five minutes later when Mark Hughes was adjudged to have clattered into the back of Matty Fryatt which resulted in referee Mike Dean awarding a penalty which was despatched by Steve Howard on a day he returned to the club he left eight years ago.
That was the signal for Leicester to turn up the heat and they had a series of chances in the build up to the break, with Howard chipping Chris Dunn after 35 minutes only for Liam Davis to clear the danger, while Jack Hobbs saw a header from an Oakley free-kick go narrowly wide.
The second half was a continued story of Leicester pressure with Dunn saving a shot on the turn by Fryatt, while a poor back header by Crowe almost let in Leicester's top scorer after 67 minutes.
Leicester finally went ahead with Dyer's clinical finish and Northampton's late rally which also saw Jackman fire wide when well placed came to nothing.