Messi's 23 goals from the last 12 games has helped him arrive at the landmark 60 figure, the first time since Gerd Muller scored 67 goals in the 1972-73 season for Bayern Munich.
With a minimum of nine games still to play in the league and cup, 24-year-old Messi has the German's record well within his sights.
Barca's victory on Saturday also helped the champions slash Real Madrid's lead to three points with Jose Mourinho's side facing a tough April schedule, starting against third-placed Valencia on Sunday.
After that comes the Madrid derby against Atletico and the El Clasico showdown with Barca also to feature.
Relegation-haunted Zaragoza took advantage of a slow start from Barca with Carlos Aranda heading them in front in the 30th minute after earlier missing a penalty.
Carles Puyol brought Barca back on level terms six minutes later and then Messi hit a double towards the end of either half, the second from the penalty spot.
In injury time, Messi set up Pedro Rodriguez for the fourth.
"All we can do is keep going and see what happens in the matches still to play. We knew this would be a difficult game for the way that the opposition has been playing in the last month and the state of the pitch made it worse for both of us," said Barca coach Pep Guardiola.
"Everyone does it to try and make it difficult for us but it also makes it hard for them as well.
"There are more fouls, the game is slower and there is more contact. They do it to all the pitches except San Mames (Athletic Bilbao), even the Bernabeu. In any case we have always won when they have kept the grass long."
Zaragoza's hopes of a comeback had been hit a minute before half time with the dismissal of Abraham Minero.
It was a new-look Barca side to that which beat AC Milan to qualify for the Champions League semi-finals in midweek with Gerard Pique missing through injury while Xavi Hernandez, Andres Iniesta and Sergio Busquets were rested.
That meant Alexis Sanchez and Pedro Rodriguez got a chance in attack.
Zaragoza, on a high after three straight wins saw them move off the bottom of the table, took the game to the champions.
Puyol and Javier Mascherano were struggling against the imposing Aranda who had his first chance after five minutes when he just failed to connect with a cross from Ruben Micael.
Again Aranda was heavily involved as Zaragoza won a penalty after 23 minutes.
He latched onto a cross from Ivan Obradovic with his effort coming back off the post, and then keeper Victor Valdes failed to get to the ball before Angel Lafita brought him down.
Valdes redeemed himself though by parrying a weak spot-kick from Aranda.
Barca were slowly getting into the game when Zaragoza took the lead through Aranda after a through ball by Pablo Alvarez.
That was the spur that Barca needed and at the other end Alexis had a shot from close range blocked by keeper Roberto Jimenez.
From the resulting corner, the visitors equalised after a howler from the shot stopper. Roberto dropped the cross at the feet of Puyol who slotted home gratefully.
Minutes later, Messi turned the game on its head making easy work of going round defender Paulo Da Silva before firing into the roof of the net.
Before half-time Zaragoza were reduced to 10 men following the expulsion of Abraham for a second yellow card.
Sanchez won a penalty five minutes from the end after a foul by Javier Peredes and Messi made no mistake from 12 yards. In stoppage time, Pedro finished off a pass from Messi to give them an emphatic scoreline.
Miguel Perez ‘Michu' scored a hat-trick as Rayo Vallecano took a step closer to safety with a 6-0 thrashing of Osasuna.
Diego Costa, Emiliano Armenteros and Roberto Triguero ‘Tito' were also on target and the visitors have now conceded eleven goals in two matches following their 5-1 defeat by Real Madrid last weekend.
Getafe added to bottom side Sporting Gijon's problems with a 2-0 win thanks to goals for Nicolas Miku and Diego Castro while Espanyol came from two goals down to draw 2-2 against Real Sociedad.