On 51 minutes Achraf Hakimi scored, then Julian Brandt and finally, with 13 minutes to go, Hakimi scored the victor.
Barcelona will be without three defenders - Gerard Pique is suspended, while full-backs Nelson Semedo and Jordi Alba are injured. Previous year there was also criticism because we lost at Leganes. Meanwhile, forward Antoine Griezmann found himself on the bench.
Four minutes later, Suarez turned provider for Messi and the latter doubled Barcelona's lead after capitalising on Mats Hummels' misplaced pass. Barcelona continued to dominate and came close to adding to their lead, but Dortmund managed to hold on till half time.
Dortmund almost scored in the first minute of play, as Barcelona goalkeeper Marc-Andre ter Stegen was forced into a save on Nico Schulz with the follow-up effort going wide.
Samuel Umtiti, himself returning from a serious knee injury, can provide some cover at the back, and midfielder Ivan Rakitic is fit from an Achilles problem, having came on as a second-half substitute at Leganes. The centre-back played a ball right to Frenkie de Jong, leading to a one-two combination between Messi and Suarez that the Argentine finished off. Dortmund's resistance was finally broken when Luis Suarez was played through by Lionel Messi, before finishing past the hapless Roman Bürki.
"It is always hard to come here, and we always struggled here with 'Gladbach, but we will try to win and get a good start to the competition".
But Barcelona could be faulted for letting their guard down after the Messi goal.
Jadon Sancho pulled a goal back for Borussia Dortmund with a peach of a strike from the edge of the box, before hitting the bar ten minutes later.
Ernesto Valverde's side lead the standings with 11 points from five games, Inter Milan are second on seven while Dortmund are third, also on seven, with Slavia bottom with two.
Yellow cards: Messi (Min. 51) for Barcelona, Busquets (Min. 71) for Barcelona, Guerreiro (Min. 74) for Borussia Dortmund.