The Essex Senior League outfit took the lead midway through the first half.
Stotfold had a golden opportunity to restore parity just before the break when they were awarded a penalty for handball but the spot kick was well saved.
That’s how things stayed until a quarter of an hour from time when Stotfold twice pulled level in four minutes - Salam Amoako and Desejado Da Silva on the mark for the hosts – with the visitors striking again inbetween.
With the score at 2-2 extra time loomed but in no time at all West Essex were ahead again and this time they sealed victory in injury time with a goal that hit both posts before going in.
The Eagles return to SSML action on Saturday with a trip to Cockfosters before hosting Colney Heath in the league on Tuesday.