Isco's spot kick sent Real Betis ahead in the 38th minute, but Salas headed Sevilla level in the 56th minute, and neither side could find a winner in the La Liga affair.
The home team remain seventh in the table, two points behind sixth-placed Real Sociedad, while Sevilla stay 13th, now boasting 38 points from their 33 league games this term.
Last season's 12th-placed finish proved to be Sevilla's worst final spot in Spain's top flight since being relegated at the end of the 1999-2000 campaign, and they will therefore be bidding to improve on that this term, while Real Betis are aiming to secure more European football next season.
Sevilla are now unbeaten in their last four league games, picking up 10 points in the process, and it is seven points from the last nine available for Manuel Pellegrini's side.
Sevilla stretch unbeaten run to four matches
Real Betis came close to making the breakthrough in the fifth minute of the contest through Johnny Cardoso, but his header from an Isco corner was just wide of the post from close range.
Sevilla did have the ball in the back of the home side's goal in the 24th minute through Lucas Ocampos, but it was disallowed for offside.
Cardoso came close again for the hosts on the 30-minute mark, with his strike from inside the box requiring a smart save from Sevilla goalkeeper Orjan Nyland.
Pablo Fornals then had one cleared off the line by Sergio Ramos in the 35th minute, before Real Betis were awarded a penalty in the 36th minute, with Dodi Lukebakio being penalised for a handball.
Isco stepped up for Pellegrini's side and found the back of the net to make the breakthrough in the Seville derby, with the 32-year-old registering his eighth goal of the campaign in all competitions.
Real Betis were looking for first La Liga win over Sevilla since 2018
Youssef En-Nesyri had an opportunity to level the scores late in the first period with a close-range volley, but the forward was denied by Real Betis goalkeeper Rui Silva, as the hosts entered the interval 1-0 ahead.
Cedric Bakambu passed up the chance to make it 2-0 to the hosts early in the second period when he fired wide of the post from close range, before Nyland did brilliantly to deny Ayoze Perez in the 52nd minute.
Real Betis were made to pay for the missed chances in the 56th minute, with Salas heading a corner from Marcos Acuna into the back of the net.
The hosts were awarded another penalty in the 58th minute, with Loic Bade penalised for a foul on Isco, but following intervention from VAR, the decision was overturned by the referee.
Isco continued to cause Sevilla problems, with the playmaker being denied by Nyland in the 80th minute, before Abde Ezzalzouli hit the crossbar with a header for the hosts late on.
Both sides were ultimately made to settle for a share of the spoils, though, with Sevilla stretching their unbeaten run over Real Betis in La Liga to 11 matches, and each of the last four league fixtures between these two sides have now finished all square.