Ibrahimovic reacted with lightning reflexes to head the ball into an empty net from the edge of the penalty area to notch his 52nd goal in 102 international appearances.
Bottom of the group on a single point, Moldova chose to defend deep for most of the game and created little, their occasional forays forward on the counter-attack failing to trouble the Swedish rearguard.
Ibrahimovic almost doubled his tally in the 75th minute, but his thunderous free kick found Cebanu in a less generous mood and he swatted the ball away to safety.
Cebanu continued to redeem himself, performing a smart double-save to deny Sweden substitutes Marcus Berg and Emil Forsberg in the 81st minute.
But there was little he could do in the 84th minute when winger Forsberg was upended and Ibrahimovic smashed home the resulting penalty to secure the win for Sweden.
The gloss was taken off the victory somewhat for the Swedes when defender Andreas Granqvist was dismissed, receiving his second yellow card deep into stoppage time.
With group leaders Austria winning 5-0 away to Liechtenstein, the result means the Swedes stay in second place on nine points, four behind the Austrians.
(Reporting By Philip O'Connor; Editing by Justin Palmer)
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