Atletico also set a club record of 13 games unbeaten at the start of a season, bettering their previous tally of 12 from the 1995-96 campaign when they won a league and Cup double.
Cristiano Ronaldo scored on the rebound after having a penalty saved to give Real Madrid a scarcely-deserved 3-2 win against Malaga on Saturday while Atletico Madrid recorded their biggest win of the season by thrashing Levante 5-0.
Real twice squandered the lead at home to Malaga due to individual errors but restored their advantage for a third time in the 76th minute as Ronaldo knocked in on the rebound when his spot-kick was turned away by visiting goalkeeper Roberto, ending a domestic goal drought that had spanned four games.
Atletico took advantage of some woeful defending from their hosts, whose defender Rober Pier scored an own goal in the fifth minute while Kevin Gameiro cashed in on a dreadful attempted clearance by Chema Rodriguez to tap in the second in the 29th.
Gameiro struck again after the interval while Antoine Griezmann scored twice in the space of three minutes to complete the rout, netting for the first time in seven league games.
Atletico are third, tied with fourth-placed Real on 27 points after 13 games while Barcelona, on 34, visit second-placed Valencia on Sunday with the chance to move seven points clear at the top of the standings.
"This was a great performance from us, we began with an early goal and put them under a lot of pressure and created a lot of chances," Gameiro told reporters.
"It's great to score five goals but we have to keep working like this."
Atletico also set a club record of 13 games unbeaten at the start of a season, bettering their previous tally of 12 from the 1995-96 campaign when they won a league and Cup double.
Karim Benzema nudged in Real's opening goal in the ninth minute after Ronaldo's header came back off the bar but Malaga levelled in the 16th through Uruguayan Diego Rolan after an awful misplaced pass in the area by Real's Toni Kroos.
It was Malaga's first goal away from home in the league this season.
Germany midfielder Kroos made amends by whipping in a corner which Casemiro leaped to head Real back in front in the 21st minute, while Malaga were denied an equaliser on the stroke of halftime for a foul by defender Paul Baysse on Dani Carvajal as he headed home.
Real were without captain Sergio Ramos, who broke his nose in last week's goalless draw with Atletico Madrid.
Coach Zinedine Zidane also rested Luka Modric and benched usual number one goalkeeper Keylor Navas despite the Costa Rican returning from injury, instead keeping faith with Kiko Casilla.
Malaga pulled level again 12 minutes into the second half following two errors from Madrid. First Raphael Varane gave the ball away and then Casilla let Gonzalo Castro's shot from distance slip through his hands.
Real took the lead for the third time when Luis Hernandez tripped Luka Modric in the area, allowing Ronaldo to convert at the second time of asking.
"We started well and scored early which is important but we started giving the ball away and everything changed," Zidane told reporters.
"The second half was very difficult but we're happy with the result and need to remember we won, even if things didn't go exactly as we would have wanted."
Elsewhere on Saturday Real Betis and Girona played out a thrilling 2-2 draw with three goals in a frantic finale while Eibar won a local derby at Alaves 2-1.
