The Fifth, the most popular after the composer's First, the celebrated Classical Symphony, augurs well for future instalments.
For Alsop, Prokofiev was a man who "bucked the prevailing trends" and who had the knack of catching a unique childlike quality into his music.
Perhaps this lies behind the prankish humour of this symphony's second movement or the balletic qualities of the finale - the Fifth was written in 1944, following Prokofiev's ballet Cinderella.
The performance has been luxuriantly captured in the SPSO's own home, the Sala Sao Paulo, praised by the conductor as the most beautiful concert hall in the world.
This youngish orchestra (founded in 1954) has a magnificent string section that responds well to darker moments of the score, in which you can feel the psychological toll of life in wartime. When Alsop calls for surging arches of sound in the opening movement, the response of the strings is immediate and thrilling.
The disc is completed with a real curiosity, the composer's The Year 1941.
Is this work, a reaction to the German invasion of the Soviet Union, a "symphonic suite"? Shostakovich, for one, thought not. Rejected by the Soviet establishment and eventually recycled as film music, The Year 1941 receives an impressive resurrection under Alsop's baton.
The struggles of the times are all over the brilliant opening movement, even if the bombast of the closing For The Brotherhood of Man is less convincing. In between lies a fragile nocturne, in which we feel that masks are off and we are closer to the heart of the man who wrote it.
Stars: 4/5
Verdict: "American maestra launches promising Prokofiev down South America way."