Barca took full advantage of Real Madrid's defeat to Athletic Bilbao on Saturday with a hugely convincing win at Camp Nou.
Suarez claimed his side's first and final goals, while Messi scored three times in the space of 12 second-half minutes to register a record 24th hat-trick in La Liga.
"Suarez and Messi are having more and more chemistry, and today we all saw what they bring to the team," said Barca coach Luis Enrique.
Barca now hold a one-point advantage over Real, having reached the Copa del Rey final in midweek.
"We are where we wanted to be, but in the final of the Copa del Rey just one [team] will go home happy, in the league just one will go home happy and in the Champions League it will be the same," Luis Enrique added.
"We have to keep playing well and win every match.
"The objective is to lead at the end of the season."
Barca were aided by the 54th-minute dismissal of Rayo defender Tito for a foul on Suarez, which gave Messi the opportunity to open his account with a retaken penalty.
Dani Alves saw red for the hosts with 10 minutes remaining, but by that stage the result was beyond doubt.
