Carlo Ancelotti's side dropped two points in the title race but extended their lead to four points over bitter rivals Barcelona, third, who host Athletic Bilbao on Sunday.
David Alaba's own goal sent the hosts ahead but Madrid quickly pulled level through Dani Carvajal.
Madrid faced their legendary former captain Sergio Ramos, back at Sevilla, for the first time in 18 years, and he gave a typically all-action display to frustrate Los Blancos.
Sevilla impressed, giving as good as they got in new coach Diego Alonso's first match in charge, ahead of their Champions League clash with Arsenal on Tuesday.
Despite Rodrygo's struggles in front of goal, having failed to score in the previous 10 matches, Ancelotti paired him with Vinicius Junior up front.
They faced off against Ramos, 37, who rejoined his boyhood club Sevilla in September and put in a heroic defensive display at the raucous Ramon Sanchez-Pizjuan stadium.
Madrid struck early through Fede Valverde but the goal was disallowed for offside against the division's top scorer, Jude Bellingham.
At the other end Carvajal cleared off the line, Kepa Arrizabalaga thwarted Lucas Ocampos and Djibril Sow flashed a strike just wide of the far post.
It was an end-to-end clash, high on tension and excitement, even as both teams struggled to find the breakthrough.
Ramos produced a stunning block as Alaba tried to turn home from close range and later squared off with his Madrid successor, Antonio Rudiger, squeezing the German's cheeks.
Sevilla goalkeeper Orjan Nyland saved Vinicius' volley before the break, one of Madrid's clearest chances.
The goalkeeper then denied Rodrygo early in the second half with a superb save with his legs, as the visitors hunted for the breakthrough.
Ramos, in his element, produced multiple blocks and clearances to keep Madrid at bay, before Sevilla took the lead.
Alaba, under pressure from Youssef En-Nesyri, accidentally turned Ocampos' cross into his own net with 15 minutes remaining.
However the Andalusians were not able to hold on to their lead for long, with Carvajal heading Toni Kroos's free-kick home at the near post four minutes later.
Tempers frayed in the final stages as Vinicius pushed Nyland, who exaggerated by falling to the floor, sparking a shoving match between both sides, who could not be separated.
