Southend twice had the ball in the net in the opening 45 minutes.
Anthony Straker pounced at the back post after five minutes and just before half-time Gavin Tomlin headed home for the visitors - referee Darren Deadman ruling both efforts offside.
Fleetwood grew in confidence in the second half and created a number of good chances, with David Ball unable to get a shot away following Barry Nicholson's cross.
Jamie Milligan then swung in a cross from the left but Junior Brown was unable to make contact.
Steven Gillespie could have snatched it for the home side late on, but his shot from nine yards sailed over the bar.
Fleetwood were given a late scare when Freddy Eastwood's late shot was deflected over, goalkeeper Scott Davies eventually gathering the ball from the resulting corner to see out the draw.