Messi - who scored Barca's second goal - is now on 35 league goals, well placed to beat the record of 50 he himself set last season.
The Argentinian four-time world footballer of the year is also closing in on the 300-goal mark for Barca with his tally at 299.
Barca have 62 points from 23 games, which leaves them on course to beat Real Madrid's record of 100 points from last season, while they could also better Real's record of 121 goals, also from last season, having so far netted 78 times.
Barca are 12 points ahead of Atletico Madrid, who were due to visit neighbours Rayo Vallecano later on Sunday. Atletico are four up on Real, who caned Sevilla 4-1 on Saturday.
Camp Nou was almost packed to full capacity with 85,610 attending for the Barca win.
In addition to Messi, Alexis, David Villa, Cristian Tello, Andres Iniesta and Gerard Pique all scored for Barca.
Assistant coach Jordi Roura was again standing in for head coach Tito Vilanova, who will stay in New York for treatment for his throat cancer for another two weeks.
Roura was full of praise for man-of-the-match Iniesta, saying: "I would not dare to say it was his best game ever for Barca, because he has turned in so many wonderful performances over the years."
Roura also praised Alexis, who scored his first league goal of the season, and thus ended his poor run of form.
The Chilean striker said afterwards: "I know what class of player I am and what I can do. Until today, I was getting into good positions but failing to finish properly. Now this is going to change," Alexis said.
Meanwhile, Iniesta said: "We really enjoyed ourselves today, and I think the crowd did too. It was good to score at the end, but it doesn't really matter who scores in this team," Iniesta said.
Getafe coach Luis Garcia was full of praise for Barca, saying: "When you play at home against them it is different, but here the difference is massive."
"You just don't know what to do against them. We tried to stop them, but it is very difficult."
Later on Sunday, Athletic Bilbao and Zaragoza slipped down towards the relegation zone with demoralising home defeats.
Bilbao crashed 4-0 against lively Espanyol, Zaragoza lost 2-1 against Real Sociedad.
Bilbao are sixth from bottom with 26 points, the same as Granada.