Out-and-out chances were few and far between in the first period, but five minutes before half-time Plymstock were denied by a point-blank save by the Lakeside goalkeeper before smashing the rebound against the post.
The breakthrough did finally come mid-way through the second half when Brannon Roberts drilled the ball into the bottom corner of the net from the edge of the box.
And the three points were sealed in the final five minutes when Mark Loudon scored with a fine header from a corner, before Anastasiou scored a second with another low shot into the corner of the net.
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