Leicester were gifted a first-half lead when Kari Arnason put through his own net only for Argyle to level before the interval courtesy of Craig Noone.
After a languid start, the game sprang to life around the half-hour mark. First, Pilgrims forward Rory Fallon had a goal-bound effort blocked after Noone had broken free on the left to set him up with a low pass across the six-yard box.
Leicester responded immediately with a swift break led by Lloyd Dyer. He created space for a shot that beat Argyle goalkeeper David Stockdale but cannoned back into play off a post, just beyond the reach of City striker Martyn Waghorn.
Leicester did not have to wait long until they took the lead, although they played precious little part in the goal.
City defender Jack Hobbs sent an aimless ball forward that was not within 20 yards of a team-mate, but Arnason, under no pressure, got his communication with Stockdale all wrong and lobbed his back-pass into an unguarded net.
Argyle were not behind for long, equalising when Chris Clark's right-wing cross into the penalty area picked out Noone and he sent a looping header over City goalkeeper Chris Weale and into the net.
Leicester twice went close after the interval. Paul Gallagher, playing against his former club, had a shot blocked at the last by Chris Barker. Then Waghorn wriggled clear of the Argyle defence inside the penalty area and sent in a shot across the goal that dribbled only just inches wide.
City later missed a golden opportunity to take the lead when Bruno Berner sent a free header wide from barely five yards after Gallagher's fine cross.
Argyle responded with a dipping long-range shot from Joe Mason that Weale just managed to tip on to the crossbar before Hobbs headed a long-range shot from Carl Fletcher off the line as Leicester survived the late onslaught to grab a share of the spoils.