Peterborough will face the Baggies at home in the FA Cup fourth-round replay on Wednesday evening.
Nicholas has backed the League One outfit to win at the ABAX Stadium and knock out Premier League side West Brom.
“There's a great incentive for Peterborough and they always score goals, just one less than League 1's leading scorers, and London Road, which always has a great atmosphere, will be rocking,” the former Celtic forward wrote on Skysports.com.
“West Brom just don't do well in the cup competitions, they won't prioritise this game because of their league troubles and I can see the Posh prevailing.”
A footnote added: “Charlie predicts: Peterborough to win 2-1 and Jon Taylor to score first.”
Peterborough will have home advantage for the replay, but it is still a shock prediction from Nicholas. After all, Graham Westley’s side in League One, while West Brom are a Premier League outfit.
The outcome of the game will depend on the team that Baggies manager Tony Pulis fields against the Posh.
West Brom will head into Wednesday’s game on the back of a 1-0 defeat to Newcastle United away from home at St. James’ Park in the Premier League.
Peterborough won at the weekend, getting the better of Chesterfield 1-0 away from home at the Proact Stadium in League One.