The Prema Racing driver extended his lead in the standings in Saturday’s sprint - having lined up third - after winning the feature race in Monaco last weekend.
He took second from Jak Crawford (Hitech) around the outside of Turn 1, briefly making contact, before passing polesitter Amaury Cordeel (Invicta Virtuosi) for the lead on the second lap.
Despite the tricky conditions, Vesti was able to build a 5.3s lead before the safety car, which saw the field dive into the pits to switch from wet to slick tyres.
The safety car period ended with two laps remaining, and though Theo Pourchaire swept past his ART team-mate Victor Martins for second on the penultimate tour, it was Vesti who held on for the win.
The race had a rolling start as heavy rain fell on the Circuit de Barcelona-Catalunya, with Vesti moving around Crawford at Turn 1, the latter suffering a puncture and dropping down the order, though the stewards judged there was no action necessary.
Further back, Pourchaire tussled with DAMS driver Ayumu Iwasa, the Japanese driver narrowly avoiding the gravel.
Vesti took the lead on lap two at Turn 10 after Cordeel ran too deep, before Martins passed the Belgian on lap four at Turn 1.
Pourchaire, who had lined up ninth, was up to sixth by lap four, passing Doohan for fifth on lap 11 around the outside of Turn 12.
Cordeel then dropped further back, having fallen to fifth on lap 11 before he ran wide at Turn 8 the following tour, allowing Pourchaire into fifth.
With 10 laps remaining, conditions were improving, and several drivers began to pit for the slick tyres, though they struggled initially to get temperature into their tyres.
The safety car was deployed on lap 20 after Juan Manuel Correa (Van Amersfoort Racing) went into the gravel at Turn 2, with those who were yet to stop opting to switch tyres.
With racing resuming four laps later, Vesti cleared a 1.2s gap out front, as Pourchaire took third from Hauger on the inside of Turn 1.
He then made it past his team-mate next time round, taking the fastest lap, but was unable to catch Vesti.
Hauger finished fourth, with Doohan in fifth and Richard Verschoor in sixth for Van Amersfoort Racing.
Sunday polesitter Oliver Bearman (Prema) and Iwasa rounded out the points-paying places.
