Diego Simeone's men were not at their best at Vicente Calderon, though they ultimately claimed a victory that keeps them in the hunt at the top of the table.
Tiago put Atletico ahead in the 12th minute as he nodded in Koke's corner, before Antoine Griezmann got the second just before the break.
Malaga improved after half-time and pulled one back through Roque Santa Cruz, but Diego Godin headed in to seal the win.
Tiago believes the victory over a Malaga side who had won their five previous games in La Liga proves how good the champions really are.
"We are very happy," the Portuguese midfielder told reporters. "We came up against a great team who plays very good football in Malaga. They came with a lot of confidence after five wins and we knew it would be very difficult. But we have proven to be a great team.
"The fans know that we give everything on the field. This year is not easy and on Wednesday [against Olympiacos in the UEFA Champions League] we have a very important game and it's great that the fans are with us."
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