Bradley Smith had converted pole into an early race lead, before being passed by Nicolas Terol on lap 2 of 23.
Terol, Smith and Corsi then broke away from the rest of the field, with Corsi holding a clear advantage by the closing stages.
With Corsi's Jack & Jones Aprilia team-mate Terol safe in second, in front of his home fans, attention turned to the fight for the final podium position, with Smith and Stefan Bradl battling right to the line.
Polaris World Aprilia rider Smith held off Bradl by just 0.036secs to claim his first podium of the season - and second ever in grand prix racing - to put his Qatar disappointment behind him.
But world champion Gabor Talmacsi's nightmare start to the season continued as the Hungarian - twelfth at Qatar - retired with mechanical problems on lap three, while holding fourth position.
Aspar Aprilia team-mate and Qatar race winner, Sergio Gadea, crashed out of 18th not long after. Danny Webb also hit the ground, and was seen nursing an injured wrist as he walked away.
Race results - Jerez:
1. Corsi (Aprilia)
2. Terol (Aprilia) +3.206secs
3. Smith (Aprilia) +4.986secs
4. Bradl (Aprilia) +5.022secs
5. Nieto (KTM) +6.254secs
6. Bonsey (Aprilia) +20.563secs
7. Redding (Aprilia) +22.517secs
8. Aergerter (Derbi) 23.002secs
9. di Meglio (Derbi) +23.928secs
10. Cortese (Aprilia) +33.541secs
Webb (Aprilia) DNF