Aguero and Rodri both struck in the opening half hour with City in dominant form.
But Mbwanna Samatta’s late first half effort gave the Villans a shot in the arm and made for a compelling second half.
And it needed a stunning late save from Claudio Bravo, who pushed Bjorn Engels 88th minute header onto a post to maintain our lead
However City, with Phil Foden producing a dazzling display, deservedly saw the job through to seal a hat-trick of League Cup wins following our triumphs in 2018 and 2019.
City came into the game on the high following our superb Champions League win at Real Madrid in midweek, but it was Villa who made the initial early running.
Dean Smith’s men carved out the game’s first opening, Anwar El Ghazi rising at the back post to send a powerful header just over.
However, thanks to our calm, possession-based approach, City quickly warmed to the task and Sergio Aguero was inches off target with a deft back header from Ilkay Gundogan’s eighth minute pinpoint cross.
And that patience paid dividends on 20 minutes as that man Aguero – who else – made the all-important breakthrough.
Within five minutes City almost struck again.
Foden, deployed wide on the right and a constant threat on the ball, latched onto a stunning 45-yard cross-field Oleks Zinchenko ball before cutting inside and dispatching a drifting effort which slid just wide of the far post.
But on the half hour our growing dominance was rewarded once more as Rodri doubled our advantage.
It was an old school effort – a bullet header from Gundogan’s inviting corner – but a thing of beauty in itself!
With City looking irresistible, only a desperate block from Villa’s Tyrone Mings then kept out a goal-bound Raheem Sterling drive
But then, against the run of play, Villa narrowed the deficit on 41 minutes to get right back into the contest.
El Ghazi evaded defensive cover on the left flank before arrowing in an inviting cross which Mbwana Samatta powered home with a spectacular diving header.
City looked to reassert control after the break with the ever dangerous Foden seeing a 52nd minute 15-yard half volley narrowly miss the target.
The introduction of Kevin De Bruyne approaching the hour only added extra vim and verve to City’s work.
But, with just a goal in it, the game remained on a knife-edge - especially with Villa’s aerial threat and physicality.
We almost had that crucial third on 74 minutes, Rodri again powering in a header from a De Bruyne but Villa keeper Orjan Nyland produced a superb save to keep the effort out.
Claudio Bravo then produced a late moment of magic, the City keeper pushing Bjorn Engels' goalbound header onto the post in a nerve-shredding finale.
But City held firm to secure another deserved piece of silverware.
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STATS AND MILESTONES
City have now won six consecutive English trophies
It’s our seventh League Cup success (70, 76, 14, 16, 18, 19, 20)
Guardiola has now won 21 of the 25 finals he has overseen as a top-flight manager – including six with City (one FA Cup, three League Cups and two Community Shields).
We have now progressed or won the final of each of our last 19 domestic English cup ties (FA/League Cup).
It's now five League Cups in seven years!
MAN OF THE MATCH: PHIL FODEN
A virtuoso display.
Touch, vision, technique – he possesses everything needed to scale significant footballing heights.
He set up the opener with a beautiful cushioned header and was central to everything we did thereafter.
It marked a fifth Carabao Cup success for the City trio – a truly remarkable record of achievement and the perfect testament to their supreme talent, stamina and staying power.
All three have been key cornerstones of our League Cup triumphs in 2014, 2016, 2018, 2019 and now 2020.
A special landmark for three extra special players.
The national stadium is becoming a real home from home for City and playing at the iconic venue seems to bring the best out of Pep Guardiola’s side.
Today’s victory marked our eighth successive victory at Wembley across all competitions – a run that stretches back to our Carabao Cup final win in 2018.
And with City still very much in the hunt as we seek to defend our FA Cup crown, there could yet be another trip to the capital later this season.
City are back in action on Wednesday evening when we switch attention to our defence of the FA Cup.
Pep Guardiola’s squad will make the short trip across the Pennines for a fifth-round clash away to Championship side Sheffield Wednesday.
Kick-off at Hillsborough is 7.45pm
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