Striker Jarvis has only made three starts this season but was called into action with 10 minutes remaining and a draw looking inevitable, but the former Norwich player had other ideas.
It was deep into five minutes of injury-time when he met a cross from fellow substitute Jason Crowe to send a sublime header past Peterborough goalkeeper Joe Lewis to seal the points for the home side.
Orient, with on-loan defender Adam Barrett making his 500th League start, had gone ahead after 67 minutes when their former defender Gaby Zakuani stabbed a Stephen Dawson cross past his own keeper from eight yards.
However, Peterborough substitute Nathaniel Mendez-Laing equalised just four minutes after coming on. His first involvement was to rise highest to meet a Grant McCann corner from the right and head the ball into the roof of the net from 12 yards.
With 10 minutes remaining, Posh striker George Boyd squandered a wonderful chance to give his side all three points when he stabbed the ball wide from six yards with the goal at his mercy, allowing Jarvis to steal the headlines.