Straightforward Lampard tucked in James Milner's cross not long after the restart before Edin Dzeko cleared in a pass from Jesus Navas, who included a fierce drive.
Yaya Toure changed over a punishment after Lampard was tripped by Kamil Zayatte.
He was sent off as Dzeko's header, Jose Angel Pozo's presentation objective and an alternate Lampard strike sank the Owls' 10 men.
Match realities
Manchester City scored seven objectives in a League Cup tie for simply the third time in their history.
Sheffield Wednesday surrendered more than six objectives on a Wednesday without precedent for their history.
Few would have anticipated a seven-objective scoreline at the break after Championship side Wednesday stood their ground in a tight first half.
Head League champions City put on a slow first-half show, however were a totally distinctive recommendation after the break as they cleared aside the terrible guests to set up a last-16 tie against Newcastle.
When ex-England midfielder Lampard changed over at the close post, City's trusts of a resolve boosting win never looked in uncertainty.
Draws against Arsenal and Chelsea, punctured by thrashings against Stoke and Bayern Munich, have seen Manuel Pellegrini's side falter lately.
So the home tie against the Yorkshire side introduced the chance to restore some conviction - which they appropriately accomplished.
Manchester City's players celebrate
Manchester City supervisor Manuel Pellegrini guaranteed his first trophy in English football by lifting last season's Capital One Cup. Objectives from Yaya Toure, Samir Nasri and Jesus Navas fixed a 3-1 win against Sunderland in March.
Numerous top-flight sides field debilitated groups in the early adjusts of the League Cup, however Pellegrini named a solid beginning XI as City hunt down their first win since beating Liverpool on 25 August.
Toure captained a side pressed with internationals, including any semblance of Lampard, Dzeko, Navas and Milner, who awed again with his vitality and quality in the last third.
The Owls are sixth in the Championship in the wake of losing one and only of their opening 10 matches in all rivalries and played with a demeaner of trust in the first half.
They were not reluctant to submit players forward when they sensed the opportunity yet were not able to genuinely test home manager Willy Caballero.
Furthermore that demonstrated exorbitant as City scored three objectives in seven minutes after the restart to put the diversion past them.
Who is Jose Angel Pozo?
Source: Manchester City's official site
Marked from Real Madrid in ahead of schedule 2012, he was named for City's Academy Player of the Year grant in his first full season at the club.
The Malaga-conceived player marked his first expert contract at City in July 2013.
The 18-year-old's most loved player is Zinedine Zidane.
He persisted through a harm hit 2013-14 season, showing up in all rivalries.
Lampard opened the scoring with an auspicious landing in the close post, then Dzeko lost his marker to gather Navas' cross and drill into the far corner.
That was immediately trailed by Navas' pounding completion from inside the Owls territory, before Zayatte was released after he bumblingly felled Lampard in the punishment zone, with Toure discovering the bottom corner with the spot-kick.
With the amusement won, Pellegrini presented 18-year-old Spanish striker Pozo, who touched base from Real Madrid's foundation two years back.
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Lampard a critical player - Pellegrini
However City declined to take any kindness on Wednesday's exhausted side. Dzeko netted his second with a towering header from left-back Aleksandar Kolarov's ideal cross, before Pozo opened in an alternate Navas pass.
Also Lampard netted his third objective in four days, in the wake of balancing against previous club Chelsea on Sunday, to send City into the last 16.
Manchester City supervisor Manuel Pellegrini:
"I think it was exceptionally imperative for Frank Lampard to score once more. He's an extremely vital player.
"I said after the diversion against Chelsea that he's an imperative player for our group.
"Possibly he's currently 36 years of age and he can't play three recreations in succession however he's a top player."
Sheffield Wednesday supervisor Stuart Gray:
"We had a seven-moment frantic period where they scored three objectives. It simply demonstrates the inlet between the Championship and a main four Premier League group.
"They're world-class players and each misstep we made in that seven-moment period we got rebuffed.
"I think two of the objectives we were most likely in their half and doled a messy pass out.
"After the sending off it was harm confinement."
Edin Dzeko scores for Manchester City
Edin Dzeko's prop implies the Bosnian has scored 10 objectives in 11 League Cup recreations for City
Spanish teen Jose Angel Pozo scopes home City's sixth on his presentation
Spanish teen Jose Angel Pozo scopes home the sixth objective on his City debut
Sheffield Wednesday manager Stuart Gray
Stuart Gray viewed his Sheffield Wednesday side lose just their second match of the season
LINEUP, BOOKINGS (2) & SUBSTITUTIONS (6)
Manchester City
13 Caballero
03 Sagna
11 Kolarov
20 Mangala Booked
26 Demichelis
25 Fernandinho (Boyata - 70' )
18 Lampard
42 Y Touré (Pozo - 64' )
07 Milner (Sinclair - 73' )
15 Jesús Navas
10 Dzeko
Substitutes
01 Hart
04 Kompany
12 Sinclair
22 Clichy
38 Boyata
75 Bytyqi
78 Pozo
Sheffield Wednesday
43 Kirkland
18 Zayatte Dismissed
02 Buxton
03 Mattock
15 Lees
19 Maghoma
10 Maguire
07 May
08 Palmer (Helan - 70' )
14 Coke (Dielna - 61' )
24 Madine (Nuhiu - 61' )
Substitutes
01 Westwood
06 Semedo
09 Nuhiu
11 Drenthe
17 Helan
28 Hope
35 Diel
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