The Spain international rounded off a nice team move for the first and did likewise after exchanging passes with Gabriel Jesus for the second.
Stoke barely registered a chance all evening as their winless run stretched to a seventh match, while Man City are now two wins away from the title.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ederson; Walker, Kompany, Otamendi, Zinchenko; Fernandinho, D.Silva, De Bruyne; Sterling, Jesus, Sane
SUBS: Bravo, Danilo, Stones, Gundogan, Laporte, B.Silva, Toure
STARTING XI: Butland; Bauer, Zouma, Martins Indi, Stafylidis; Badou, Cameron, Allen; Shaqiri, Jese, Choupo-Moting
SUBS: Haugaard, Shawcross, Johnson, Adam, Fletcher, Ramadan, Crouch
Paul Lambert: "On any given day you can win a game of football. In a one-off game you can win, and that is the beauty of football. We'll do everything we can to try to win. If we try to play football the same way they do then we will be beat - that is the reality. We have to have an idea of another way to try to beat them."
Pep Guardiola: "It's almost done. But we are not the champions. The champions are still Chelsea. We have to get the points as soon as possible, knowing that we have the opportunity. I know everyone wants to anticipate the situation and what will happen, everyone is thinking about when we will win the title."
STOKE CITY SUBS: Haugaard, Shawcross, Johnson, Adam, Fletcher, Ramadan, Crouch
MANCHESTER CITY SUBS: Bravo, Danilo, Stones, Gundogan, Laporte, B.Silva, Toure