Atletico were up against it after Wissam Ben Yedder deservedly put the hosts ahead in the first half at the Ramon Sanchez Pizjuan.
But Simeone deployed Koke in a new role to stifle the Sevilla attacks and helped lead a second half fight back.
Antoine Griezmann levelled matters with a stunning free-kick for his eighth La Liga goal of the season to earn Atletico a hard-earned draw.
Speaking after the game, Atletico boss Simeone was keen to laud the impact of his midfield general.
"You could see that they were hurting us down their right flank," said Simeone, with Jesus Navas and Joris Gnagnon having proven a handful.
"We changed Koke's position because tactically he's extraordinary. He did a great job in a position he's not used to. After that, everything changed."
Koke is a crowd favourite at the Wanda Metropolitano having spent his entire career with the club, making more than 300 appearances since making his debut as a 17-year-old in 2009.
The draw meant Simeone's side, whose only top-flight defeat this season came against Celta Vigo at the start of September, missed a chance to wipe out the three-point gap to Barca ahead of the champions' trip to Getafe.
However, they did at least maintain their two-point advantage over their third-placed hosts following an entertaining clash in Seville.
Despite failing to apply maximum pressure on leaders Barcelona, Simeone was nonetheless pleased with the display from his players.
"It was a great game," he added. "Sevilla are very strong at home and there were periods in which both teams dominated.
"We didn't attack very well in the first half but we improved greatly after the break. I think the way in which we reacted deserves praise."
Next up for Atletico is a trip to Girona in the first leg of the Copa Del Rey last 16 on Wednesday.
They return to La Liga action against Levante at the Wanda Metropolitano next Sunday.