Ipswich extended their unbeaten home record in the league this season to 15 games but they could not break down a resilient Plymouth side.
The hosts dominated for long periods but a combination of poor finishing, bad luck and dogged defending ensured they failed to score.
The visitors could have snatched victory but Steve MacLean saw his second-half penalty saved.
Tommy Miller, returning to the Ipswich starting line-up, had a ninth-minute shot blocked by Mathias Doumbe.
Plymouth keeper Luke McCormick was called into action after 12 minutes to keep out Owen Garvan's effort, then at the other end Peter Halmosi shot wide from the edge of the box.
Jonathan Walters, who passed a late fitness test, saw his fierce 25-yard drive blocked by Doumbe before Halmosi again blazed wide.
Alan Quinn, making his Ipswich debut after signing from Sheffield United, saw his 25-yard effort comfortably held by McCormick midway through the half before Garvan shot wide when well placed.
Danny Haynes shot over the crossbar from 12 yards out and moments later David Wright's cross was headed over by Walters as Ipswich started to dominate.
Ipswich goalkeeper Neil Alexander had to be alert after 37 minutes to save Halmosi's free-kick while at the other end Garvan's effort was blocked by Krisztian Timar.
In first-half stoppage time Pablo Counago should have broken the deadlock but his effort went wide of the left post.
Plymouth boss Paul Sturrock made a change at half-time with Luke Summerfield replacing Yoann Folly, who had started in midfield in place of Ipswich transfer target David Norris, left out of the squad with speculation surrounding his future.
The first chance after the interval fell to Dan Harding but the Town defender sent his long-range effort harmlessly over the bar.
Quinn should have marked his debut with a goal in the 50th minute but he headed Jason De Vos' cross wide of the target.
Three minutes later the hosts spurned another glorious opportunity to take the lead. First Alex Bruce headed Garvan's corner goalwards only for Paul Connolly to clear and the ball then broke to De Vos who shot straight at Gary Sawyer.
Argyle's record signing MacLean, back into the attack for Jermaine Easter having been cup-tied at the weekend, had his spot-kick saved by Alexander after Harding was penalised for handball.
Walters tested McCormick once again with an effort from David Wright's cross before Rory Fallon forced Alexander into a good save from close range.
The chances continued to come thick and fast, with Walters firing wide 18 minutes from time and Miller calling McCormick into action.
Moments later Miller had another golden opportunity but contrived to shoot wide from 12 yards.
Substitute Easter headed wide before Counago headed Wright's cross against the post but neither side could break the deadlock.
Teams:
Ipswich Alexander, Wright, Bruce, De Vos, Harding,Haynes (Lee 72), Miller, Garvan, Quinn (Roberts 84), Counago,Walters.
Subs Not Used: Supple, Naylor, Legwinski.
Plymouth McCormick, Connolly, Timar, Doumbe, Sawyer, Clark,Nalis, Folly (Summerfield 46), Halmosi (Easter 68),Fallon (Hodges 80), MacLean.
Subs Not Used: Abdou, Jutkiewicz.
Booked: Timar.
Att: 20,095
Ref: Tony Bates (Staffordshire).