Disappointing when well-fancied for last year's renewal of the Group Two contest, Ralph Beckett's four-year-old returned as a 25-1 shot, despite running well to finish third in the Coral Marathon at Sandown on her latest appearance.
Pat Dobbs sent his mount straight to the lead from the off and she remained just about in front racing inside the final furlong.
She looked beaten when Aljezeera claimed the lead under Frankie Dettori, but Alyssa roared back tenaciously to get up by half a length.
Aljezeera was joined on the line by 9-2 joint-favourite Melodic Motion, a stable companion of the winner, with the pair dead-heating for second.
Beckett was claiming the prize for the second year in succession following the victory of Simple Verse, the 2015 St Leger winner, 12 months ago.
Dobbs said: "I couldn't see what was going on behind me, but Ralph told me to let her enjoy herself.
"When you start pulling she doesn't really enjoy it, so I let her do her own thing. She settled and was watching the Jeep in front for most of the way, so that helped. She's very honest and tries very hard.
"She's not very big but she stays well and I'd say on faster ground she'll be even better."