Ibrahimovic's 63rd-minute strike - his third of the week - proved to be the winner.
Mallorca had won 12 of 13 matches at home coming into this game, having only lost to Sevilla previously, and they can feel somewhat unlucky not to have led at the break after hitting the post twice in the first period.
Barca coach Pep Guardiola told Marca: "We knew that if we did not play in an aggressive and intense fashion, we would not win.
"Mallorca had their chances, but we defender very well, and this is how we must play for the rest of the campaign. Ibrahimovic was very important, not only because of the goal, but also his play throughout the game.
"We will check on Iniesta tomorrow, although it does not seem too serious."