Chuba Akpom gave the visitors the lead with an impressive strike but Adi Viveash's men hit back twice to give them an advantage ahead of next Thursday's second leg
Chuba Akpom gave the Gunners the lead in emphatic style on 56 minutes but the Blues levelled the match three minutes later with Charlie Colkett firing in.
And Alex Kiwomya completed to home side's comeback on 66 minutes to ensure Chelsea will head to the Emirates Stadium next Thursday with a slender lead to protect.
Blues boss Adi Viveash welcomed back Isaiah Brown and Dominic Solanke to his starting XI after the pair helped England qualify for the European Championship finals in Malta this summer.
The Arsenal team, meanwhile featured the likes of Gedion Zelalem and Akpom.
Both teams took time to find their rhythm but it was the Gunners who carved out the first clear chance of the match on 13 minutes.
Ainsley Maitland-Niles left Fankaty Dabo in his wake with a rapid surge down the right flank before cutting inside and working a space to shoot, but he screwed his effort well wide.
Chelsea responded and Colkett’s cute dinked pass found Solanke in space in the penalty area, but the striker’s attempted square pass to Kiwomya was cleared.
On 25 minutes the Blues did test Joshua Vickers, with the Arsenal goalkeeper making two good low saves in quick succession from Colkett and Kiwomya after a flowing one-touch move.
Chelsea were winning the midfield battle but Akpom forced Mitchell Beeney into action with a fierce shot from a tight angle on 31 minutes, with Zelalem missing the ball completely on the rebound.
On the stroke of half-time Zelalem’s dangerous free-kick was met by the head of Alexander Iwobi, but Beeney tipped over the winger’s looping header to leave the game goalless at the break.
Chelsea started the second half with intent and after Jordan Houghton had robbed Zelalem in the Arsenal half, Brown advanced on the Gunners defence and tested Vickers with a low shot.
At the other end Beeney was almost left red-faced five minutes later when his attempted pass went straight to Daniel Crowley, but the Arsenal midfielder was unable to get a shot away.
Arsenal did take the lead on 56 minutes, with Akpom racing onto a Maitland-Niles pass, jinking pas Ola Aina and ripping a shot high past Beeney at his near post.
Chelsea took just three minutes to respond, with captain Ruben Loftus-Cheek leading a swift counter-attack and eventually dinking the ball through to Colkett, who lashed in.
With the game opening up Brown then had Vickers at full stretch to parry out his low shot, with Solanke slicing the rebound into the side netting.
But Chelsea went in front on 66 minutes when Loftus-Cheek’s clipped cross found Solanke. The striker’s header was straight at Vickers but Kiwomya acrobatically hooked in the rebound.
Arsenal pushed forward in search of an equaliser but with the pace Kiwomya and substitute Jay Dasilva on the flanks it was Chelsea who posed the greater threat on the counter-attack.
On 83 minutes Dasilva's cross eventually found Solanke, whose point-blank shot was well blocked by Vickers, and two minutes later Dabo stung the Arsenal goalkeeper's palms with a fierce drive.
But Chelsea failed to capitalise on their late dominance and the Gunners will feel a comeback is well within their reach in front of a home crowd at the Emirates Stadium next Thursday.