Beavon had a chance of his own eight minutes later after driving towards the edge of the Pompey box, but his effort whistled wide of the post.
Portsmouth had a sight of goal after 20 minutes when Jed Wallace met a bouncing ball on the edge of the box, but his effort was high and wide.
Alex Wynter was also wasteful for Pompey after 52 minutes, as the defender could not convert past McLaughlin from close range.
Burton had their second minutes later when Lucas Akins expertly finished into the bottom corner from outside of the box.
Portsmouth continued to press as the match approached the final 20 minutes, with Hollands firing an effort just wide of the post, before Beavon hit one straight at Paul Jones down the other end.
Both sides had half chances in the latter stages, but Portsmouth could not break the deadlock despite six additional minutes.