Injury-ravaged Blackpool sprung a late surprise with the inclusion of veteran central defender Matt Jackson, signed just hours before the game on a loan deal from Watford.
He rarely put a foot wrong alongside another veteran Jackson, Blackpool captain Michael, at the heart of the home defence.
Plymouth made a bright start, forcing a series of early corners, but the first real chance fell on eight minutes at the other end of the field, where Shaun Barker's fine run from right-back was picked up with a quality delivery from David Fox, but Barker could only lift his volley over the bar.
Plymouth had a golden opportunity of their own on the half-hour mark when Swedish midfielder Peter Halmosi burst into the box and struck a shot which Paul Rachubka could only deflect into the path of Sylvan Ebanks-Blake.
But the former Manchester United striker could only find defender Stephen Crainey on the line and the former Scotland international was able to clear the danger.
There was another gilt-edged opportunity for the Seasiders five minutes before the break when Wes Hoolahan fed Fox, who beat the Plymouth offside trap and was bearing down on Luke McCormick's goal, but didn't show the necessary coolness and, instead of taking a touch, his attempt at a first-time lob left the ball high and wide of the goal.
The home side also had a decent penalty shout turned down when Andy Morrell went down under the challenge of Marcel Seip.
Keith Southern came closest to winning it for Blackpool halfway through the second half when his glancing header from Barker's high-quality cross had McCormick beaten but could only hit the post.
Plymouth threw on on-loan Manchester United youngster Lee Martin while another sub, veteran Barry Hayles, gave Rachubka a rare moment of action when his 20-yard shot had to be turned around the post.