Paulinho's 40 million-euro signing from Guangzhou Evergrande was just one of a number of much-criticised moves by the Barca board following the departure of Neymar to Paris Saint-Germain.
But the Brazilian international showed his worth by smashing home Lionel Messi's through ball to score the winner.
I'm very happy to score the goal. It was the winner which was the most important thing," Paulinho told Barca TV.
"It was a difficult game because Getafe have players with quality and we conceded the first goal but we were calm, had patience and went looking for the result."
Barca had barely replaced Dembele with Gerard Deulofeu before they fell behind six minutes before half-time.
Sergi Roberto's headed clearance fell invitingly for Gaku Shibasaki, who made his name with two goals against Real Madrid in last year's Club World Cup final for Kashima Antlers, to thunder an unstoppable dipping volley beyond Marc-Andre ter Stegen.
Valverde made another change at the start of the second period as Denis Suarez replaced Iniesta.
And it was the substitute who inspired Barca's revival as he collected Roberto's cut-back from the right wing before bending the ball high past Vicente Guaita into the top corner.
Paulinho completed the comeback when he burst onto Messi's through ball and smashed across the despairing Guaita into the far corner.
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