Determined to bounce back after Saturday’s disappointing defeat at Bournemouth, Mikel Arteta’s side gained control of the contest early on, with Riccardo Calafiori and Leandro Trossard both missing the target with a pair of good chances.
The hosts continued to probe for a breakthrough and their persistence was duly rewarded in the 29th minute when Gabriel Martinelli’s low effort rebounded off the post and into the net via an unfortunate touch from Shakhtar keeper Dmytro Riznyk.
The one-way traffic showed no signs of slowing down with half-time approaching, as only a superb piece of last-ditch defending from Mykola Matviyenko denied Kai Havertz a simple tap-in from point-blank range.
Gabriel Jesus also came close to doubling Arsenal’s lead before the break but the Brazilian’s tame strike was thwarted by the legs of Riznyk.
The Gunners’ profligacy in front of goal continued to prove problematic at the start of the second half, with Trossard glancing a header wastefully wide and Martinelli seeing a powerful effort repelled by Riznyk.
Those missed opportunities gave the visitors belief heading into the final half-hour, however, Arsenal were handed another golden chance to put the game beyond doubt when Valeriy Bondar was punished for handball in the box.
Trossard assumed the responsibility from the spot but Riznyk came to Shakhtar’s rescue again, diving to deny the Belgian.
That set up a fascinating finale, and the visitors came agonisingly close to a dramatic leveller in stoppage time, only for David Raya to save brilliantly from Pedrinho’s sharp strike, earning the Gunners a narrow but crucial victory.
Flashscore Man of the Match: Mykola Matviyenko (Shakhtar Donetsk)
