The match appeared to be drifting towards a goalless draw before Coutinho unleashed a dipping, curling effort from 25 yards out to hand the visitors an unlikely three points.
And the win for Liverpool will have eased the pressure on Liverpool manager Brendan Rodgers after the Reds lost 6-1 at Stoke on the final day of last season.
The visitors began the game with five players who had featured in that drubbing back in May, while Rodgers also handed debuts to the likes of Christian Benteke, Nathaniel Clyne, Joe Gomez and James Milner.
Stoke boss Mark Hughes, on the other hand, gave first starts to former Barcelona attacker Ibrahim Afellay and defender Glen Johnson, against his old team, although Bojan Krkic was not fit enough to feature as he continues his recovery from a serious knee injury.
However, in stark contrast to last season’s goal fest at the Britannia, the opening period was stale and lacklustre as both teams made a cagey start to the contest, although Stoke will still have been disappointed not to have gone in ahead at the break.
The Potters’ first good opening came after just eight minutes when the ball broke kindly to former Liverpool midfielder Charlie Adam, however, the Scot scuffed his shot when really he should have at least hit the target.
And 10 minutes before half-time Stoke – in front of the watching Xherdan Shaqiri in the Britannia stands – had an even better chance to break the deadlock through right-back Johnson on his first start for his new team.
The lively Jonathan Walters fed Marco Van Ginkel down Stoke’s right flank and after the Dutchman’s deflected cut-back had been cleared off the line by Martin Skrtel, the ball was fed back to Johnson, only for the former Liverpool full-back to blaze over from six yards out.
That glaring miss – Johnson’s last goal for the Reds actually came against Stoke at Anfield back in December – meant the two teams went in all square at the break, unlike in their last meeting when Stoke were 5-0 ahead at the interval.
The visitors knew they had to improve in the second period after not having a shot on goal in the opening 45 minutes, despite some nice touches from their £32.5m signing Benteke, and they did.
However, Rodgers’ side were still grateful to goalkeeper Simon Mignolet for keeping the scores level after the Belgium international produced a fine reflex save to keep out Mame Biram Diouf’s close-range effort after 64 minutes.
Thereafter, Liverpool appeared to grow in confidence, with the Reds finally having an effort on target through centre-back Dejan Lovren midway through the second half, before Coutinho gave notice of his intent by going on a mazy dribble through a posse of Stoke players, only for his goalbound effort to be blocked by the home defence.
Both sides opted to make full use of their benches, with Rodgers handing new boy Roberto Firmino his Liverpool debut in place of the impressive Jordan Ibe for the final 12 minutes of the evenly-contested encounter.
But it was Firmino’s compatriot who settled matters as, like he did on so many occasions, the little midfielder produced a moment of brilliance to light up the Britannia and break Stoke hearts.
Picking up possession of the ball midway in Stoke’s half, Coutinho turned past Steve Sidwell before beating Stoke ‘keeper Jack Butland with a sensational long-range strike worthy of winning any game.
Stoke City: Butland (6), Johnson (7), Cameron (6), Muniesa (8), Pieters (6), Van Ginkel (7), Whelan (6), Walters (7), Adam (6) Afellay (7), Diouf (7).
Subs: Odemwingie (6), Sidwelln (6), Wollscheid (6).
Liverpool: Mignolet (7), Clyne (7), Lovren (7), Gomez (7), Skrtel (8), Milner (6), Coutinho (9), Henderson (6), Lallana (6), Ibe (8), Benteke (7).
Subs: Firmino (6), Can (6).
Man of the match: Philippe Coutinho (Liverpool).