Beattie eased the pressure with two goals in a 12-minute spell, with on-loan Sunderland striker Anthony Stokes heavily involved.
Beattie's clever reverse early in the game almost broke to Danny Webber, who cut inside before finishing with a low drive that was turned round the far post by Romain Larrieu's outstretched foot.
Plymouth caught United on the break, winning a corner, midfielder Luke Summerfield's teasing cross reaching Krisztian Timar and he powered a stinging header over the target from eight yards.
Full-back Kyle Naughton prodded a teasing centre across the face of the Plymouth goal with no-one on hand to add the finishing touch, before Beattie squandered a half-chance, firing wide from a Stephen Quinn corner.
United, using a three-man attack probed again, Stokes' right-foot strike from the edge of the area being pushed round the foot of the post by Plymouth's French keeper.
The visitors finally crumbled in the 47th minute, the lively Stokes being bundled over in the area by full-back Chris Barker and Beattie coolly dispatched the penalty for his fourth of the season.
Beattie added a second 12 minutes later after Stokes has been brought down by midfielder Summerfield 25 yards out, the ex-Everton striker despatching the free-kick into the bottom right-hand corner of the net.
The United striker almost completed a hat-trick in the dying minutes, his low strike being blocked on the line after substitute Billy Sharp had rounded the stranded Larrieu.