Atletico strikers Antoine Griezmann, Fernando Torres and Kevin Gameiro all found the net as Diego Simeone's side warmed up for next Wednesday's visit to the Nou Camp.
Elsewhere, Las Palmas maintained their excellent start to the campaign by beating Malaga 1-0, and Sevilla's 15-month wait for an away victory continued after they were held to a 1-1 draw at nine-man Eibar.
Messi sidefooted in a simple cross from Suarez to strike the opening goal for Barca after 15 minutes and returned the favour for the Uruguayan to nudge in the second in the 31st.
Neymar stretched Barca's lead to three goals on the stroke of half-time, tapping in another lay off from Suarez, before Messi got his second from the penalty spot 10 minutes into the second half.
Rafinha rounded off the most comfortable of Barca victories with a curled finish in the 64th minute, although Gabriel Appelt salvaged a goal for the Madrid minnows in the 80th with a free-kick whipped into the top corner.
Barcelona, beaten 2-1 by newcomers Alaves last weekend in their first loss at the Nou Camp since April 17, now have nine points from their first four La Liga games.
They join Real, who can go clear again when they play at Espanyol on Sunday, and Las Palmas at the league's summit, while Atletico are one point behind.
"This is an important victory against a team that we knew would cause us problems in bringing the ball out. We exploited the space well and we were very active from the start," said Luis Enrique.
After squad rotations backfired against Alaves, Luis Enrique picked a similar team to the one that battered Celtic 7-0 in the Champions League on Tuesday in Barca's biggest ever win in European soccer's top competition.
Atletico kickstarted their league campaign last week with a 4-0 win at Celta Vigo and raced out of the traps against Sporting, Gameiro feeding Griezmann to tap in the opener in the second minute before curling in another in the fifth.
Griezmann then cut inside to lash in the third goal in the 31st before being replaced by Torres, and the homegrown Atletico hero further delighted the Vicente Calderon by rounding off the victory with two late strikes, including an injury-time penalty.
"We knew we were doing the right things to score goals," Torres told BeIN Sports after a rewarding afternoon for Atletico's strikeforce.
"It's good that all the forwards contributed with the goals and that I could do that from the bench. It's never a good time to visit Barcelona but now we can go there feeling confident."
Las Palmas surrendered their 100 percent record last week by losing 2-1 at Sevilla with two late strikes but got back to winning ways with a narrow win over Malaga, courtesy of midfielder Momo's penalty in the ninth minute.
At Eibar, Luciano Vietto scored his third goal in four games to put Sevilla ahead in the 27th minute and the Europa League holders looked on course for a first away win since May 23 2015 when the hosts' goalkeeper Yoel was sent off in the 45th minute.
Former Real Madrid midfielder Pedro Leon, however, levelled midway through the second half from close range to extend Sevilla's search for that elusive away win, while Eibar midfielder Dani Garcia was also given a straight red card late on.
(Reporting by Richard Martin, editing by Alan Baldwin)
