There was little to choose between the sides in terms of possession but as coach Clive Allen later pointed out, the difference was in the final third.
Birchall made no mistake with his and Arsenal's two clear-cut opportunities while we missed having a recognised striker in our line-up despite the efforts of midfielders Jamie O'Hara and Mark Yeates up front.
Stuart Taylor was still the busier of the keepers with three decent saves, Danny Karbassiyoon had to head off Arsenal's goal line and, most crucially, we struck the crossbar at the start of the second half with the score at 1-0.
In a typically feisty derby encounter, Johnnie Jackson tested Taylor as early as the fourth minute - his 20-yarder too hot to handle but no-one was close enough to tap in the rebound.
Jackson's corner almost found its way into the net via Francesco Fabregas' bizarre header but Karbassiyoon was alert on the line.
Dean Marney, lively in that first period, clipped another effort just over but we were hit by the sucker punch five minutes before the break as David Bentley sent Birchall clear to drill past Lars Hirschfeld.
An early response in the second half would have tipped the scales back in our favour but Marney was left cursing his luck as first Taylor managed to block his volley from close range and then his header from the rebound bounced agonisingly on the top of the bar before falling safely behind the net.
Taylor was soon out quickly to deny Yeates but a minute later - 59 on the clock - the visitors doubled their lead.
Fabregas did all the work, twisting and turning his way past a number of challenges all the way to the six-yard line before allowing Birchall to tap home.
OJ Mabizela forced another fine save out of Taylor from Jackson's free-kick after 63 minutes and that was the last of the chances.
Line-ups: Spurs: Hirschfeld, Kelly, McKie, Bunjevcevic, Mabizela, Marney, Hughes, Jackson, Ricketts, O'Hara (Malcolm, 61), Yeates. Unused subs: Eyre, Lee, Daniels, Wright.
Arsenal: Taylor, Bailey, Nicolau, Hoyte, Simek, Cregg, Bentley, Fabregas, Birchall (Shiels, 82), Bradley (Larsson, 87), Karbassiyoon. Unused subs: Fowler, Holloway, Djourou.
A clinical strike in each half from Arsenal's Adam Birchall settled an evenly-contested reserve derby on Monday night.