City made it nine games unbeaten at home in Europe after this victory which was only secured with the third goal after Poznan had got back into the game after looking second best for much of the first half.
Adebayor got his first goal of the season after 13 minutes then doubled his tally on 25 minutes as City dominated their Polish opponents in the first half at Eastlands.
Lech Poznan actually had the first chance of the game when Nigel de Jong allowed Slawomir Peszko to break clear and shoot wide but the tempo of the game was set a minute later as Adam Johnson fired across the face of the Poznan goal.
City continued to press and took the lead after some neat interplay allowed Adebayor to turn the defender and pass the ball into goal.
Poznan showed their mettle on the break and tried to get back into the game with half chances from set pieces.
But an early goal from the visitor’s early in the second half pushed City onto the back foot and only when Adebayor clinched his hat-trick on 72 minutes did the home side regain the initiative.
With City hesitating as Poznan claimed for a penalty the ball broke to Joel Tshibamba who finished from close range much to the delight of the vociferous 5,000 Polish supporters.
The Congo forward should have levelled on 69 minutes but blazed over as City were rocking.
But a moment of class from Silva calmed the City nerves and allowed them to regain the initiative.
A slide rule pass from the Spaniard into the path of Adebayor was finished easily to make him the first Manchester City player to score a European hat-trick.
Adam Johnson hit the woodwork after a wonderful solo run and Adebayor had two more chances to add to his tally.
At the other end defensive lapses could have brought Poznan back into the game, a frailty Mancini will want to quickly address.
Man City scorers: Adebayor 13, 25, 72
Lech Poznan scorers: Tshibamba, 49
Referee: Alexandru Dan Tudor (Romania)
Venue: City of Manchester Stadium
05 Zabaleta (Bridge 85)
08 Wright-Phillips (Jo 77)
11 A Johnson
21 Silva (Yaya Toure 75)
34 De Jong
42 Yaya Toure,
05 Arboleda (Djurdjevic 69)
19 Bosacki (yellow card)
07 Wilk (Stilic 55)
15 Drygas (Rudnevs 55)