But the Catalans withstood an exciting final spell to move effectively to within seven points of their 25th league title.
Ernesto Valverde's side lead their nearest challenger, Atlético Madrid, by 14 points, with Diego Simeone's team hosting Levante and fourth-placed Real Madrid visiting bottom-placed club Málaga on Sunday.
"It was more important that we picked ourselves up after a hard week and the players have showed great attitude today and stepped up".
Barca's procession towards the league title continues on Tuesday as they travel to Celta Vigo, before the Copa del Rey final against Sevilla next weekend.
"It was three important points really, for a lot of reasons", said Valverde.
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But it should take little away from their faultless form in the league, which means the last time they tasted defeat outside a cup competition was against Malaga just over 12 months ago.
"I've already decided what I will do", Iniesta said in the mixed zone of the Nou Camp.
A awful back-pass from Barca nearly went pear-shaped as it freed in Rodrigo, who took a touch before forcing Ter Stegen pushing his shot to the crossbar for a corner.
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Barcelona doubled its lead six minutes into the second half.
The comeback plans were hit hard after Barca went two up off a header by Samuel Umtiti, with Neto unable to keep it out despite his best efforts on 51 minutes.
Dani Parejo came close with a 35-yard free-kick but captain Andres Iniesta could have made it 3-0, with Neto reacting well to parry his volley from Lionel Messi's cross.
But, in the 86th minute, Jose Gaya was brought down in the box by Ousmane Dembele and Daniel Parejo managed to score the resulting penalty past Ter Stegen, who nearly saved the effort.
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