A 26th minute goal from debutant Remi Allen was enough for the hosts, who put in a dogged, yet composed, performance in front of 2,671 fans.
Following early pressure from the visitors, Blues grew into the first half with Jo Potter flashing a free-kick wide before Melissa Lawley fired over from 12 yards after Emma Byrne spilled a Chelsea Weston cross.
The hosts were turning in an assured performance and got their rewards when Allen gave them the lead. Full-back Weston put in another right-wing cross, but this time she picked out the former Lincoln midfielder who swept the bouncing ball into the far left corner from 12 yards out.
With confidence growing Blues looked to increase their lead, but Kirsty Linnett saw Caroline Weir clear her effort off the line as the hosts went into the half-time break with a one-goal advantage.
Arsenal started the second half brightly and when Kelly Smith switched the play to Alex Scott, she nodded inside to Shinobu Ohno, but the Japanese international was denied by a heroic last-ditch Aoife Mannion tackle.
The visitors continued to put the pressure on the hosts, but David Parker’s side closed them down quickly at every opportunity to deny Arsenal a clear effort on goal.
With just three minutes remaining, the visitors wasted their best chance.
After being set free down the left flank, England international Smith whipped a wicked ball into the Blues box, but Ohno volleyed her first-time effort high into the Tilton Road stand from eight yards out to ensure Blues did not concede a crucial away goal ahead of Sunday’s second leg.
Birmingham City Ladies XI: Spencer; Weston, Mannion, Harrop, Carter; Carney, Allen, Moore, Potter, Lawley; Linnett (Simpkins, 79)
Unused subs: Baggaley, Sargeant, Keryakoplis, Simpkins, Wilkinson, Torkildsen, Haines.
Goal: Allen (26)
Arsenal Ladies XI: Byrne; Scott, Mitchell, Stoney, Kinga; Weir, Bailey, Ohno; Carter, Smith, Yankey (Ayisi, 77)
Unused subs: Chamberlain, Hoogendijk, Williamson, Bragg, Sampson, Humphrey
Booked: Smith, Carter, Kinga