Mane put the ball past the onrushing Jose Sa after the title-chasing Reds fell to a shock lead to Pedro Neto's goal in the second minute.
But Mane owes a huge debt of gratitude to Thiago, whose genius flick wrong-footed the Wolves defenders and left the Senegal international through on goal.
And former Liverpool star Jamie Carragher was left marvelling at the Spain international's brilliance.
"Mane's the scorer but Thiago's role in the goal is absolutely sensational," Carragher said on commentary for Sky Sports.
"That guy's got the eyes in the back of his head and this just illustrates it.
"It isn't the best connection from Sadio Mane but that is out of this world from Thiago."
That goal put Liverpool back on track and belief that they could win a second Premier League title was renewed when Manchester City went 2-0 down thanks to goals from Matty Cash and former Red Philippe Coutinho.
However, a heroic comeback from Pep Guardiola's men saw them run out 3-2 winners and seal City their sixth Premier League title.
Goals from Mohamed Salah and Andy Robertson ensured Liverpool did their job but City's win meant that proved academic.
Liverpool still have plenty to play for as they meet Real Madrid in the Champions League final.
However, they may be without Thiago for the clash with Klopp saying the 31-year-old is 'not good' ahead of the clash in Paris.