At the end of a first half featuring few genuine chances for either team, Jonathan Walters had given the Potters an advantage with a firm near-post header a minute before the break.
But the visitors were much improved in the second 45, with the introduction of Coutinho and Firmino after the interval helping to reverse the scoreline.
The Brazilian duo struck within two minutes of one another, while Simon Mignolet thwarted both Charlie Adam and Saido Berahino with stunning saves to secure three points.
The key points…
- Walters headed Stoke in front late in first half
- Coutinho restored parity midway through second period
- Mignolet denies Adam and Berahino at close range
- Sensational Firmino blast snatched important win
The team news…
Jürgen Klopp opted for three changes and a switch in formation, with Trent Alexander-Arnold, Joel Matip and Ben Woodburn – for his first Premier League start – brought into the line-up.