Villa were far superior to Saints in the first half, and could have scored more than two in the opening period, but a fine early finish from Ollie Watkins and a slick team goal just before the break put the hosts in command nonetheless.
There was no letting up after halftime as Coutinho, who delightfully set up Douglas Luiz for Villa's second, then got in on the act, showing quick feet before finding the net to put the game to bed seven minutes into the second half.
Danny Ings' side-footed finish two minutes later put the result beyond all doubt, with Villa able to take their foot off the gas for the remainder of the match.
A second successive victory moves Villa up to 11th in the standings, two points behind Southampton in ninth after Ralph Hasenhuettl's side suffered their first defeat in eight in all competitions.
While several Villa players were on top form, it was Coutinho who drew special praise from coach Steven Gerrard - a former team mate of the Brazilian at Liverpool.
The Barcelona loanee has been directly involved in six goals in four home Premier League appearances for Villa - three goals and three assists.
"We've got Phil (Coutinho) back fit and in a really good place - he was back to his Liverpool form today and he was a touch above," Gerrard told the BBC.
"The other players have got a lift from him. It is about having players running in behind for him and Ollie Watkins and Danny Ings were untouchable at times today too.
"When Phil is in the mood he is a world class player. He probably finished my career a couple of years early, he's the reason I've got screws in my knees and groins!"
Hasenhuettl felt it was just one of those days for his side who had been in great form coming into the match.
"We couldn't compete today - we weren't good enough in the duels," he told Sky Sports. "We had problems with the shape and it was too easy to concede goals today.
"It was the first time in a long time we haven't scored a goal and we weren't sharp enough today.
"It was tough after conceding a third goal and we had a few changes and it got a bit better but everything was wrong today."