Llorente put Atletico in front at the start of the second half, tearing into the box from the left wing and tucking the ball inside the near post from a tight angle.
Betis had played well in the first half and dominated the ball. However, Atletico took control of the game after Simeone hauled off Lucas Torreira and Thomas Lemar for Yannick Carrasco and Hector Herrera for the second period, instantly giving the team more pace and purpose in midfield.
"Betis made things very difficult for us and we struggled in the first half, but we went out in the second half with the same mentality and were lucky to score very quickly and that gave us oxygen," said Llorente.
"Simeone believes in us and we believe in him. We also believe in ourselves and together we make a very strong union. We made that clear today and we've got a victory we really needed."
The visitors were reduced to 10 men with 20 minutes remaining when Martin Montoya was sent off for hauling down Carrasco. The referee initially gave the defender a booking before he revised the play in a VAR review and changed it to a straight red card.
Suarez then struck in stoppage time after combining well with left back Renan Lodi to clinch a therapeutic victory for Atletico after Wednesday's 4-0 thrashing by Bayern Munich in the Champions League.
It was Suarez's fourth goal in five league games for Atletico, tying him for the La Liga lead.
The win took Atletico, who are unbeaten in a club record 21 games in La Liga, into second in the standings on 11 points after five games, two behind Real Madrid who beat Barcelona 3-1 earlier on Saturday in the "Clasico."