By then Alexander had been banished to the stands by referee Carl Boyeson for protesting after Posh fell behind to a twice taken 74th minute penalty by Hasney Aljofree.
This was just the performance Alexander was seeking after a disastrous five-match losing streak, Posh producing a workmanlike first-half showing against a Plymouth side 42 places above them.
Posh were first to emerge from the early midfield exchanges with Richard Butcher seeing an eighth minute effort deflected behind by Gary Sawyer.
The resulting corner brought problems for Posh with Ben Futcher suffering a facial injury as he flung himself to reach Jamie Day's flag kick and after a lengthy spell of treatment the lanky defender was replaced by Guy Branston.
Josh Low, making his Posh debut after signing from Leicester City in a £100,000 midweek deal, lifted a shot a foot over the Plymouth bar when Day squeezed through a low cross.
A game of honest endeavour rather than FA Cup passion badly needed a player to open things up and the Pilgrims looked to have found the answer in Akos Buzsaky, who hit both Posh posts in the space of ten minutes before the break.
The Hungarian midfielder, once signed by Jose Mourinho during his time at Porto, slammed a 30-yard shot across Mark Tyler and against the home goalkeeper's right-hand post, before rattling the opposite stick after Tyler pushed away a close-range shot from Cherno Samba.
Despite lacking suspended top scorer Barry Hayles and with other absentees through injury, Plymouth became more adventurous in the second period.
One of Ian Holloway's stand-ins, 18-year-old Rueben Reid stormed to the heart of the Posh defence and was stopped only by a fine challenge from Adam Newton.
Reid later had penalty appeals waved aside, but by then Plymouth were down to ten men with Paul Connolly sent off for a second bookable offence.
The Pilgrims retained the attacking initiative and grabbed the lead on 74 minutes with Aljofree keeping his cool at the penalty spot after Peterborough-born David Norris had been brought down by Branston.
A plastic bottle appeared to be thrown at Plymouth players as they celebrated in front of home fans, but Alexander had hardly reached his seat in the stand before Mclean, who completed a £150,000 move from Grays last weekend, forced the tie into a replay.
He drove the ball low past goalkeeper Luke McCormick after Low cut the ball back into the middle of the area.