Fleetwood's day got worse when Jeff Hughes spurned the chance to equalise by firing over the crossbar from the penalty spot.
However, Jon Parkin rescued the Cod Army in the final minute of the match, netting his third goal in as many games to earn a 1-1 draw.
Exeter City failed to take advantage of their rivals dropping points. The Grecians, who could have gone level on points with the leaders by beating Hartlepool United, lost 3-0 at home to the Monkey Hangers, who have now won three away games on the spin in all competitions.
Oxford United, Morecambe and Rochdale all climbed above Exeter. The U's recorded a 2-0 home win over Northampton, while the Shrimps won 2-0 at Bury and Rochdale thrashed Newport County 3-0 at Spotland.
Burton Albion topscorer Billy Kee was sent off just before half time at the Pirelli Stadium, where the Brewers managed to keep Southend United at bay until the final minute when Freddy Eastwood stole all three points for the Shrimpers.
Alan Bennett struck four minutes from time to earn AFC Wimbledon a 1-1 draw with Accrington Stanley, while Alfie Santos found the net late on as Bristol Rovers took a point from their trip to Mansfield Town.
Results in full: Plymouth 1-1 Portsmouth, AFC Wimbledon 1-1 Accrington, Burton Albion 0-1 Southend, Bury 0-2 Morecambe, Dag & Red 1-2 Cheltenham, Exeter 0-3 Hartlepool, Fleetwood Town 1-1 Chesterfield, Mansfield 1-1 Bristol Rovers, Oxford Utd 2-0 Northampton, Rochdale 3-0 Newport County, Wycombe 3-2 Torquay Utd