Atletico Madrid stayed eight points adrift of Barca at the top with 3-0 win over Deportivo la Coruna thanks to goals from Saul Niguez, Antoine Griezmann and Angel Correa.
Juan Rodriguez's own goal opened the scoring at the Camp Nou yesterday, before Messi saw his penalty saved by Vicente Guaita, teed up Munir El Haddadi and Neymar and smashed home his 36th goal of the season all before half-time.
Neymar and Arda Turan rounded off the scoring to seal Barca's 12th straight La Liga win after the break.
An eighth defeat in nine games leaves Getafe just a point above the relegation zone.
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"This is a unique team, different to the rest and which does things that make it seem like there is nothing the opponent can do," said Barca boss Luis Enrique.
"It is a great pleasure to be in this position."
The European champions weren't even at full strength as Enrique left Luis Suarez on the bench ahead of Barca's return to Champions League action against Arsenal on Wednesday.
Barca's one fallibility this season was exposed moments later when Neymar was chopped down by Emiliano Velazquez inside the area.
Messi took responsiblity, but for the ninth time in 20 spot-kicks Barca failed to convert, as Guaita dived to his left to turn the five-time World Player of the Year's effort to safety.
Neymar's display had been under scrutiny after he took
advantage of being suspended for last weekend's 4-0 win at Eibar to fly back to Brazil to celebrate his sister's birthday.
Messi then took out his frustration at not netting from the spot to rifle home the fourth from outside the box five minutes before half-time.
The pattern continued after the break with Messi in generous mood with another clinical through ball for Neymar to sweep home his 25th goal of the season.
And Turan added a sixth just before the hour mark with an acrobatic overhead kick which left Guaita flatfooted.
Atletico also warmed up for their crucial Champions League clash with PSV Eindhoven on Tuesday with victory as they eased past an under-strength and out of form Deportivo.
"The important thing is the goals are coming from all over the pitch," said Simeone.
"That makes us more unpredictable because we can create chances from anywhere."
Niguez opened the scoring with a powerful header from Filipe Luis's cross after 18 minutes.
The hosts were completely dominant and should have doubled their lead before half-time as Yannick Carrasco fired straight at German Lux before Griezmann slotted wide a gilt-edged opportunity.
Carrasco crashed a shot off the post just after the break, but Griezmann did finally make the game safe when he slotted into the far corner for his 23rd goal of the season.
Elsewhere, Celta Vigo bounced back from their 7-1 thrashing at the hands of Real Madrid last weekend as Iago Aspas's early winner moved them up to fifth with a 1-0 win over Real Sociedad.