Xavi described the decision to force the Blaugrana to play as "crazy" after they were hit with a spate of COVID-19 cases during the mid-season break, but his makeshift side coped admirably against Luis Garcia's men.
De Jong, who had already hit the woodwork twice, headed in his second league goal of the campaign in the 44th minute to seal just a second win in Barca's last six games across all competitions.
The result moved the Catalan giant up to fifth – one point behind fourth-placed Atletico Madrid – while Mallorca remains in 15th.
Barca looked more lively than its host in the early stages and went close through Gerard Pique's free-kick and Ferran Jutgla's whipped strike.
De Jong twice went agonisingly close to opening the scoring moments before the half-hour mark, first poking against the post from Ilias Chakkour's pass and then crashing a spectacular bicycle kick off Manolo Reina's crossbar.
The striker was not to be denied shortly before the interval, though, rising highest at the back post to head home Oscar Mingueza's cross and give Barca a deserved half-time lead.
Barca continued to do much of the pressing after the break, with Pique and De Jong going close to grabbing a second.
But it was ter Stegen who became the late hero of the piece, superbly keeping out Jaume Costa's stoppage-time volley as Xavi's side held on to claim a 12th win from its past 13 away LaLiga games against Mallorca.
Both sides are in Copa del Rey action on Thursday (AEDT), with Barca travelling to Linares Deportivo and Mallorca visiting Eibar.