The Gunners will face more questions about their defensive frailties ahead of the new season after this result.
Arsene Wenger had kept captain Cesc Fabregas out of the squad, accepting speculation over his future left the Spain midfielder "unsettled" with Barcelona looking to take their former trainee back to the Nou Camp.
Arsenal, though, showed little sign of missing their talisman as summer signing Gervinho impressed to set up Robin van Persie for the opening goal on 27 minutes, with Aaron Ramsey doubling the lead at the start of the second half.
However, the Gunners once again hit the self-destruct button at the back as mistakes from Sebastien Squillaci and Johan Djourou were punished when the Argentinian side struck twice in four minutes.
While Wenger still has time to put things right before the action kicks off for real at Newcastle in a fortnight's time, Gunners fans will be hoping that comes via the arrival of a new centre-half - with Everton's Phil Jagielka a target - rather than relying on his current backline not to make the same mistakes again.
Ivory Coast forward Gervinho had impressed on his first Arsenal appearance, scoring twice in Cologne last weekend, and along with fellow new arrival defender Carl Jenkinson was named in a starting XI which also featured fit-again goalkeeper Lukasz Fabianski and contract rebel Samir Nasri, yet to sign a new deal.
The Gunners made a lively opening, and had an early penalty shout when Jack Wilshere felt he was tripped, but referee Martin Atkinson waved play on.
Gervinho darted clear down the right and centred for van Persie, whose flick was just wide.
Set-pieces proved Arsenal's weakness last season and again they looked vulnerable when Juan Insaurralde sent his free header over at a corner.
However, the hosts made the breakthrough on the half hour, Gervinho the provider. This time, the £11million forward got away down the left flank and crossed for van Persie, who slotted home at the near post.
Arsenal were now well in command of possession, youngster Emmanuel Frimpong - who missed all of last season with a serious knee injury - settling in alongside Wilshere.
Wenger made the expected sweeping changes for the second half.
Arsenal extended their lead straight after kick-off when substitute Ramsey drilled home from 20 yards after a penetrating run from Carlos Vela.
On the hour, substitute keeper Vito Mannone did well to turn over a dipping shot from Lucas Viatri.
However, the Boca Juniors striker was not to be denied on 68 minutes when he riffled the ball into the top corner after Juan Riquelme had robbed Squillaci.
Another defensive blunder allowed Boca Juniors to equalise when Djourou fell over a ball into the Arsenal penalty area and Pablo Mouche swept home.
Emmanuel Eboue, supposedly set to join Galatasaray in a £4million deal, saw a 25-yard effort fly wide.
Mannone beat away Riquelme's free-kick at the near post to prevent a total collapse.
Arsenal face New York Red Bulls on Sunday, with Thierry Henry's side having beaten Paris Saint-Germain 1-0 earlier in the day.