Messi scored his second just 6 minutes after scoring his first making it 3-1 for his side and Suarez followed suit netting once again just before halftime.
The Uruguay striker then set up Lionel Messi to give Barca the lead in the 30th minute.
With the victory, Barcelona maintains their undisputed contention for the league title by sitting comfortably at the top of the La Liga table with a difference of 10 points from second-placed Atletico Madrid.
Messi's wizardry put Ernesto Valverde's side in front on the half-hour mark, after Suarez touched down a long pass from Andres Iniesta for the Argentinian. Let us know in the comments section below. He nearly scored with a dipping shot after 18 minutes but his effort was headed off the line by Bernardo. Benzema had snapped a run of almost three months without a league goal by scoring against Real Betis last weekend and was one of Real's best performers in their fifth consecutive win in all competitions. Goalkeeper Bono was unsighted and the ball rolled past him.
Messi nearly put Barcelona ahead after 19 minutes after Suarez had picked him out in the box. Finally, Suarez got the hat-trick to cap off the evening of goals after tapping in a cross from Ousmane Dembele.
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Human Rights Watch said the apparent destruction of homes erases evidence for legal claims from the exiled Rohingya . Free speech will be a key issue for those concerned about human rights this year, the report said.
And Coutinho got in on the act in the 66th minute with a brilliant Barca fifth from 25 yards.
Barca's record signing turned on the edge of the penalty box before curling a shot around Bono.
Messi's assist for Suarez's opener was his 148th in La Liga and he has now created and scored more goals than any other player in the league's history.
Girona's players were applauded by Barca fans for their efforts.
The Argentine has now scored against 36 different clubs in the La Liga to break the League record.
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