The German surprisingly left both on the bench in favour of youngsters Ben Woodburn and Trent Alexander-Arnold but with Liverpool trailing at halftime to a Jonathan Walters header he reverted to Plan B despite fitness worries over both.
Coutinho equalised with a low shot 20 minutes from time and less than three minutes later Firmino scored a superb lob to seal victory and boost Liverpool's chances of finishing in the Premier League's top four.
They remain third, nine points ahead of fifth-placed Arsenal and sixth-placed Manchester United, both of whom have three games in hand on Klopp's side.
Klopp said Firmino was suffering from exhaustion after his recent long-haul trips to play for Brazil, while Coutinho had lost three kilos due to illness in the past week.
"At halftime it was a difficult decision to make because it was not clear that Roberto and Phil would be ready for 45 minutes," Klopp told a news conference.
"Phil lost three kilos in the last three days. For most of us that would be good news! But for Phil and a professional football player, it is not as good. He came to the hotel this morning and said 'I'm fine'.
"But we knew he would have a low energy level, full enough for 30 minutes."
Read the full article on eurosport.co.uk: Klopp's Brazilian masterstroke seals 'massive' win at Stoke