The 22-year-old forward brought coach Pep Guardiola and the Nou Camp faithful to their feet when he collected Maxwell's pass just after the half hour and smashed a shot on the turn into the top right corner.
Barca have 18 points from six matches, matching their best start to a league campaign, and are three ahead of arch rivals Real Madrid.
The Portugal forward sprained his right ankle in Wednesday's 3-0 Champions League win over Olympique Marseille.
Guardiola included Pedro in his team in place of the injured Thierry Henry and the home side dominated the early stages at the Nou Camp with their trademark slick passing.
Almeria goalkeeper Diego Alves did well to deflect a Xavi volley on to the post in the 18th minute after good work from Sweden striker Zlatan Ibrahimovic on his 28th birthday and Pedro's follow-up bounced off the same upright.
Barca were unable to exert the same dominance in the second period, with a hard-working Almeria side chasing every ball, but although the visitors managed to string together several good moves they did not come close to finding an equaliser.