It may be too late to salvage City's defence of the Premier League title as they remain 14 points behind runaway leaders Liverpool, who also have a game in hand, but led by Aguero the champions moved ahead of Leicester into second to show they will not give up the chase.
Aguero eclipsed Thierry Henry's record as the top scoring non-English player in the Premier League by taking his tally to 177 goals and also surpassed Alan Shearer's league record for hat-tricks with his 12th since joining City from Atletico Madrid in 2011.
"He was a legend and the legend rises tonight," said Guardiola. "He is one of the most incredible players I've seen in this league.
"To score this amount of goals and hat-tricks means you have done for many, many years a lot of good things.
"You have to be consistent for many years so it's an incredible compliment to him."
Guardiola could afford the luxury of recalling Aguero among six changes to the side that also outclassed Manchester United in midweek to put one foot in the League Cup final.
Villa could be their opponents at Wembley on March 1 as they held Leicester 1-1 in the first leg of their semi-final on Wednesday, but on this evidence they would be powerless to stop City lifting the trophy for a third straight season.
The injury-hit hosts were without a recognised striker and first-choice goalkeeper after Wesley and Tom Heaton were ruled out for the rest of the season.
Former Spanish international 'keeper Pepe Reina was in the stands ahead of his loan move from AC Milan being completed and will be needed if Villa are to beat the drop after conceding 13 goals in their last four home games.
"It was a chastening experience," said Smith. "We are embarrassed by some of the goals we conceded today.
"We've come up against a top class team with a top class manager and got found out."
- Mahrez on the mark -
Orjan Nyland was beaten at his near post as Riyad Mahrez was allowed to cut onto his favoured left foot to open the floodgates on 18 minutes.
The Algerian's old Leicester teammate Danny Drinkwater was making his Villa debut after troubled spells at Chelsea and Burnley since leaving the Foxes.
His lack of match practice was exposed for City's second as Drinkwater was caught in possession inside his own box by Gabriel Jesus and the ball broke kindly for Mahrez to drill home his ninth goal of the season.
Aguero then thumped home a third, although Nyland could have got a stronger hand to the Argentine's effort.
All that was missing from a complete City performance was a moment of inspiration from Kevin De Bruyne and the Belgian duly delivered with a wonderful curling cross to set the fourth on a plate for Jesus in first-half stoppage time.
City did not let up after the break and could have made it many more than six as David Silva picked out Aguero to calmly slot home his record-breaking goal.
The Argentine's hat-trick arrived eight minutes from time as he demonstrated his array of finishes by this time blasting his past the helpless Nyland.
"I'm so happy for the record. It is thanks to my teammates, they help me in these nine years," said Aguero.
"When I scored the second, I thought one more (and) I break the hat-trick record. I want to keep scoring more goals."
Anwar El Ghazi scored from the penalty spot in stoppage time, but it was little consolation for Villa, who dropped into the relegation zone after Watford's win at Bournemouth earlier in the day.