The right-winger grabbed a priceless double, including his 89th minute strike, as Jay Harris had also scored in first-half injury-time.
Todd and Harris had given Stanley the lead twice in the first half, as Craig Mackail-Smith's third goal in two games had levelled the game at one apiece.
Posh full-back Josh Low then levelled the game up for a second time in the 53rd minute when he swivelled and fired home left-footed from close range.
Stanley were always the better side in this pulsating five-goal thriller, but when they missed a whole host of gilt-edged chances it looked as if three points would pass them by.
But when Todd bulldozed his way through two weak challenges down the right to get a sight of goal for his tenth of the season, the sigh of relief around the Fraser Eagle Stadium was massive.
Manager John Coleman still wants four wins from their last five games to be completely sure of safety and he also admitted that he was ready to substitute Todd two or three minutes before the end.
But Posh manager Darren Ferguson, who will be well aware that his side's play-off chances are slipping away, said that the early goal was crucial.
Accrington will now travel to league leaders Hartlepool on Bank Holiday Monday to try and grab their fourth win in five.