The visitors looked like they would go back to the Spanish capital with a point after Felipe had cancelled out Ivan Rakitic's stunning early strike.
Ocampos had other ideas, though, slamming home with just two minutes remaining to inflict a third straight top-flight defeat on Diego Simeone's men.
The result moved second-placed Sevilla five points behind leader Real Madrid, which plays Cadiz on Monday (AEDT), while defending champion Atleti is now a whopping 13 points adrift of its city rival.
One bonus for Atletico was that Real Sociedad also lost ground, losing 3-1 at home against Villarreal, thanks to superb display from Gerard Moreno, who scored two and assisted the third for the visitors.
However, Rayo Vallecano cancelled out that positive news, putting itself a point clear of Atletico with a 2-0 victory against Alaves, which continues to struggle at the wrong end of LaLiga's table.