England captain Houghton's injury-time free-kick earned City victory over Notts County while Chamberlain saved a penalty and saw another go wide as Liverpool beat Birmingham 1-0 despite Mandy van den Berg's red card.
Arsenal beat Reading 3-1 in the opening day's other game.
City looked set to have to settle for a point after a game in which both teams missed penalties, Jess Clarke for County and Toni Duggan for the reigning champions.
But Houghton's free-kick from 30 yards a minute into added time ensured all three points for Nick Cushing's side.
"We always go to the end," said Cushing
"I think the team really pulled together and wanted the goal and I think a draw would have felt like a loss."
Chamberlain, a summer signing for the Reds, denied Kirsty Linnett from 12 yards and saw Freda Ayisi miss the target after Van den Berg's dismissal
Shanice van de Sanden scored the only goal in the eighth minute
Nigeria forward Asisat Oshoala scored early in the second half of her Arsenal debut, after Dominique Janssen had given them an interval lead.
Reading debutant Jade Boho-Sayo pulled one back but Danielle Carter's header clinched victory for Arsenal.
Source : PA