After a cagey opening from both sides, Maxi Araujo smashed a left-foot shot goalwards, which David Raya somehow managed to divert onto the crossbar.
It would be 10 minutes before Arsenal even had a sniff of a half-chance, with former Sporting striker Viktor Gyökeres easily shepherded away from goal.
Noni Madueke, a replacement for the injured Bukayo Saka, then hit the bar with an effort to score an Olympic goal from a corner for the visitors.
The Portuguese side were happy to change to a back five whenever Arsenal attempted to attack, limiting the North Londoners’ momentum.
However, as the half progressed, Sporting had still not got their danger man Luis Suarez involved, and collectively the hosts had only mustered three touches in the Gunners’ area to show for their efforts.
By half-time, neither side had really imposed themselves to any great degree, though Arsenal would likely have been the more disappointed of the two teams, given they’d not made anything of nine crosses into the box.
The game quickly settled into a familiar pattern after the break, with Declan Rice in particular stopping any Sporting attacks at source.
Martin Odegaard’s floated free-kick kept Rui Silva on his toes, before Trincao’s low drive had Raya scrambling across goal.
Just after the hour mark, Martin Zubimendi looked to have given Arsenal the lead with a curling effort from outside the box, but the goal was quickly ruled out for offside.
Rice was doing more than most to ensure a positive outcome for Arsenal, as his winning back of possession on 13 occasions would attest.
With seven to play, Raya again came to the Gunners’ rescue, with a superb one-handed save from Geny Catamo’s intelligent header.
With only two minutes of injury-time to be played, there was no better moment for Havertz to silence the stadium with a low drive to win the match for the Gunners.
The result means that the Portuguese side remain winless after eight games against Arsenal (D4, L4), but the way in which they contained the Gunners for long periods will give them hope of springing a surprise at the Emirates Stadium.
Flashscore Man of the Match: Declan Rice (Arsenal)