Fryatt - sacked boss Craig Levien's last signing - pounced after Wolves keeper Stefan Postma spilled Paddy McCarthy's header.
Former Walsall striker Fryatt saw Joleon Lescott clear his first-half effort off the line after beating Postma to the ball.
Foxes keeper Rab Douglas denied Kenny Miller an equaliser with a sharp save.
Wolves manager Glenn Hoddle on Stefan Postma's fumble:
"It's always disappointing when you lose games like that.
"Stefan was the first to say it was down to him. He pulled off a great save in the first half but at this level you don't expect to concede goals like that.
"But what concerned me most was that at 0-0 we didn't show enough desire to win the game. Sometimes it has to be down to hard graft and grit but we didn't have enough players showing that, so there were harsh words in the dressing room."
Leicester: Douglas, Stearman, McCarthy, Kisnorbo, Johansson, Maybury, Gudjonsson, Wesolowski, Hughes, Hume (O'Grady 74), Fryatt.
Subs Not Used: Smith, Gerrbrand, Hammond, Williams.
Goals: Fryatt 70.
Wolverhampton: Postma, Edwards, Lescott, Gyepes, Naylor, Ricketts, Ince, Kennedy, Miller (Ganea 85), Cort (Rosa 66), Frankowski.
Subs Not Used: Oakes, Craddock, Anderton.
Referee: L Probert (Gloucestershire).