The Millers' strong arm tactics infuriated the home supporters with Richard Cresswell earning an early booking for a foul on Neal Bishop.
Barnet looked threatening down the left-hand side, mostly through Puncheon's probing runs and from one attack Birchall slotted the ball home only for an offside flag to rule the goal out.
Rotherham replied with a Stephen Brogan free-kick which whistled inches past the post and nearly took the lead on the half-hour mark when hesitance in the Barnet box saw Andy Todd almost bundle the ball home.
Bruce Dyer was then a whisker away from scoring before the Bees finally registered a shot on goal.
Nicky Nicolau played in a left-wing cross and, as the ball fell to Birchall, his strike from a matter of yards out saw Andy Warrington block with his legs.
Barnet flew out the traps after the break and should have been ahead within two minutes of the restart.
A great flowing move saw Birchall square the ball across the face of the box to Puncheon who beat Warrington but not the woodwork as his shot crashed back off the inside of the post.
However, minutes later they were in front when Bishop released Birchall and he neatly tucked the ball home.
Rotherham never looked likely to pull the scores level and Barnet wrapped up the points with seven minutes left when substitute Liam King brought down Birchall in the box.
Puncheon stepped up and confidently dispatched the spot-kick past Warrington.