Champions Atletico Madrid also moved to within two pointes of the leaders as they were 1-0 victors at 10-man Getafe thanks to Mario Mandzukic's first-half goal yesterday.
Villarreal seemed set to take all three points when substitute Luciano Vietto clipped home Cani's pass to open the scoring 11 minutes from time.
However, Suarez slotted home a loose ball inside the area two minutes from time and Bacca converted from the penalty spot deep into stoppage time after Giovani Dos Santos had upended Benoit Tremoulinas.
Villarreal enjoyed the better of the play in the first period at the Sanchez Pizjuan, but it was Sevilla who came closest to breaking the deadlock when Gerard Deulofeu's corner came back off the post.
More From This Section
Sevilla 'keeper Beto was forced to make a point-blank save from Ikechukwu Uche just before the break and the Nigerian striker should have done better when he fired wide 11 minutes into the second-half.
Uche's replacement Vietto was more clinical when handed the chance to give Villarreal the lead as he raced onto Cani's through ball to lift the ball over the advancing Beto.