Juan Sebastian Veron pulled a late goal back for the South American champions but an injury-time strike by substitute Juan Cuevas made the Argentine Clausura championship win safe for Gimnasia.
It was Gimnasia's first win in the "clasico" of La Plata since 2005 following seven defeats, one of them 7-0, and two draws.
Their ground in the Bosque (wood) was full to brimming with 22,000 Gimnasia fans. For security reasons there were no visiting supporters and 900 police officers were on duty.
The last time Gimnasia beat Estudiantes it was 4-1 at the same ground in 2005. Since then the derby had been played at the new, neutral, city-owned Ciudad de La Plata stadium eight times and Estudiantes' ground once.
Stracqualursi put the home side ahead on the stroke of half-time with a diving header after winger Diego Villar's cross had taken a deflection off Veron.
He had a penalty saved by goalkeeper Agustin Orion shortly after halftime after defender Gaston Re brought down Colombian striker Marcos Perez but his second goal 10 minutes from time seemed to have settled it comfortably for Gimnasia.
However, Veron set up a nail-biting finish with Estudiantes' goal two minutes from time.
The visitors went all out for an equaliser and keeper Gaston Sessa made a brilliant save from Enzo Perez three minutes into stoppage time.
Seconds later at the other end, Orion's attempt at kicking the ball back deep into Gimnasia territory fell to Cuevas who shot into an unguarded net.
