For coach Ernesto Valverde, the pressure eases just a little, and the fact they notched this victory without Lionel Messi and Ousmane Dembele, both sidelined with thigh injuries, is another source of encouragement.
Suarez lobbed in the 41st-minute opener, and Junior Firpo tucked in Barcelona's second from close range early in the second half for his first goal for the club. Getafe spurned first-half chances they might have gobbled up on another day and Clement Lenglet's 84th-minute dismissal for two yellow cards came too late to give them any real advantage.
Valverde fielded a front three of Carles Perez, Suarez and Antoine Griezmann. The game largely passed Griezmann by, not for the first time since his summer switch from Atletico Madrid.
Getafe were unbeaten in their last eight home LaLiga matches; however, Barcelona had won on 10 of their 14 previous visits to the Coliseum Alfonso Perez in LaLiga, more than any other visiting side.
Perez tested David Soria in the Getafe goal early on, before Suarez stabbed a shot wide following a smart throughball from Frenkie de Jong.
Barcelona's defence was then picked apart too easily, with Angel allowed space to shoot from six yards, his strike blocked by the legs of Marc-Andre ter Stegen.
Jaime Mata had a close-range effort deflect wide off Junior at the other, with Barcelona increasingly shambolic at the back. Inter will have taken encouragement.
But Suarez pounced to give Barcelona a 1-0 lead in the 41st minute when a clearance from Ter Stegen turned into a great long ball for the Uruguayan striker to chase, and he lobbed Soria in style.
Soria was culpable for Barcelona's second four minutes into the second half, as he could only push a 25-yard shot from Perez back into play, and Junior had an easy finish.
Suarez and Perez almost added to the lead, while Arthur nearly fired past Soria into an empty net after the goalkeeper went walkabout, but two was enough.
What does it mean? Barca punish wasteful hosts
It means what we already knew: that Barcelona will typically have too much firepower, if the opposition fail to take their own chances. There was little liquid football on show from the defending LaLiga champions, but a big boot downfield from their goalkeeper and a composed finish from their arch predator defined this game. Sometimes such rudimentary football will do. At other times, they will need to find a greater finesse.
Ter Stegen makes history
Incredibly, Ter Stegen's long kick that set up Suarez resulted in a first LaLiga assist by a Barcelona goalkeeper in the 21st century. It was an altogether un-Barcelona-like piece of playing out from the back.
No Messi, yet too messy
Messi typically has little direct involvement in Barcelona's defending, but whenever he is on the pitch the Argentinian hoists up the standards of those around him. Without him on Saturday, Barcelona lacked guile. It was nowhere more obvious than in their rocky rearguard where some laughable interplay played into Getafe's hands. Inter are unlikely to be as sparing with their finishing as Getafe.
Key Opta facts
- Barcelona have won 11 LaLiga games at Coliseum Alfonso Perez more than any other side.
- Junior has scored six goals in his LaLiga career, all of them against different opponents.
- Barcelona have had 10 different scorers in LaLiga this season, more than any other side in the top five European Leagues.
- Suarez has been involved in seven goals in his seven LaLiga games against Getafe (five goals and two assists).