A third straight home defeat for Villa would have meant their worst start to a league campaign at Villa Park since 1946 and they were staring down the barrel following a torrid first half.
But for all their dominance, City only had Yaya Toure's opportunist strike from Samir Nasri's corner on the stroke of the interval to show for their efforts and Karim El Ahmadi got the benefit of a questionable offside call to haul Villa level in the 51st minute.
Edin Dzeko, so often profligate throughout the match, glanced home another Nasri delivery to restore City's advantage before Leandro Bacuna registered his first Villa goal in some style with a sensational free-kick.
The home faithful were barely back in their seats from Bacuna's heroics when Andreas Weimann stole between City centre-backs Vincent Kompany and Matijia Nastasic to latch onto Brad Guzman's long clearance and prod beyond his Joe Hart with 15 minutes to play.
And Lambert praised his side's resilience in restricting City when they threatened to run riot in the first 45 minutes.
"It's a big win, it's three points for us and I'm delighted to win," he said.
"I've never questioned our work ethic or desire. We might get beaten certain games but one thing I'll never label those lads is that they don't give you absolutely everything.
"They give you everything that's in their bodies and I'm really proud of them, the way they've been performing since I've been at this club and the way they've started this year.
"The start we've had has been really, really tough with the fixtures that have been thrown at us but, as I've said, I'm proud of them.”
Lambert reserved special praise for match-winner Weimann, who combined effectively with full-debutant Libor Kozak up-front to give Kompany and Nastasic an awkward second period at the heart of City's defence and ensure the absence of injury victims Christian Benteke (hip) and Gabriel Agbonlahor (ankle) were not keenly felt.
"The thing about Weimann is that every time he's on that pitch you know what you're going to get from him," the Villa boss added.
"I thought (in the) second half him and Kovak were an absolute handful. It's not just those two – the midfield guys worked ever so hard, the back lads were excellent, the two wing-backs were great.
"We played well as a group. Every one of them was excellent."
