Atleti's Jan Oblak saved a penalty for the second game in a row when he repelled Lucas Ocampos' spot-kick in the eighth minute while Sevilla's Joan Jordan hit the bar moments later in a rampant start by the hosts as the visitors looked rattled.
Sevilla finally found a breakthrough in the 70th minute when left back Marcos Acuna headed in a cross from fellow full back Jesus Navas and the referee ignored Atletico's claims that Ocampos handled the ball at the start of the move.
Atleti still top the standings on 66 points but third-placed Barcelona can move within a point of them with a win at home to Real Valladolid on Monday. Real Madrid are second on 63 after beating Eibar 2-0 at home on Saturday.
Atletico captain Koke criticised the referee for not reviewing Acuna's goal.
"It was a clear handball for the goal and there was another handball (by Diego Carlos) which should have been a second yellow card," he said.
"We have VAR which has to be there to help out. Today wasn't our day. On other days it has favoured us, today it didn't go our way."
He added: "This is a tough defeat but we tried everything. We struggled in the first half but in the second we had chances."
Atletico had only scraped a 1-0 win over struggling Alaves in their previous fixture thanks to a late penalty save from Oblak and they again failed to offer much in attack, barely threatening Bono's goal in the first half.
They carved out a clear chance moments after Acuna had broken the deadlock when Marcos Llorente got to the byline and found an unmarked Mario Hermoso, but the defender blazed well over the bar from inside the area.
Forward Angel Correa had another chance to level in the final minutes but saw his shot saved by Bono.
But Koke said his side still fully believed they could go on and win the title.
"We don't doubt ourselves at all, this is always a difficult place to go to and anything could have happened. It's football, we still have our fate in our own hands," he said.
Coach Simeone added: "We need to keep on working and increase our intensity levels as that's what got us to this stage. La Liga's title race is always tough right until the end of the season but we have to find a way to get the players playing like they were at the start of the season."