Substitute Nosa nodded home in the 89th minute at Betis's Benito Villamarin stadium, setting off wild celebrations among the home fans desperate for success against their bitter rivals.
The draw leaves Betis in sixth place on 48 points with seven games left, still in with a good chance of qualifying for Europe, while Sevilla's bid for continental competition looks to be all but over as they remain stuck in 10th on 42 points.
"In the first half we just couldn't get into the match and they were clearly better than us," Betis defender Antonio Amaya told Spanish television broadcaster Cuatro.
"But we were able to come back from three down and we are coming away feeling very pleased with that," he added. "The fans were incredible and really gave us a boost."
Sevilla had thumped Betis 5-1 at their Sanchez Pizjuan stadium in November but had to repel some early pressure before Ivan Rakitic fired them ahead with a clever finish from a tight angle in the seventh minute.
The Croatia midfielder added a second 12 minutes later, his first double since moving to Spain in January 2011, and Alvaro Negredo made it 3-0 in the 33rd minute when he clipped a Jose Antonio Reyes cross into the roof of the net.
Betis were reeling but pulled a goal back two minutes before the break when Dorlan Pabon punished a defensive error and clipped the ball over Sevilla goalkeeper Beto.
The match turned early in the second half when Ruben Castro struck from the penalty spot to make it 3-2 and Sevilla midfielder Gary Medel was dismissed for violent conduct in the 55th minute after a clash with Jose Canas.
With a man extra and the crowd roaring them on, Betis laid siege to the Sevilla goal and got their reward with a minute left when Nigerian Nosa leaped to head the winner.
Betis, who beat champions Real Madrid 1-0 at the end of November, last took part in European competition in 2005-06 when they finished third in their Champions League group behind Liverpool and Chelsea.
They are one of many Spanish clubs to have suffered severe financial problems after years of living beyond their means and were relegated in 2008-09 before winning promotion back to the top flight two years later.
Sevilla have also fallen on hard times since blazing a trail in Europe and winning the UEFA Cup, the predecessor to the Europa League, in 2006 and 2007.