Celtic posed little threat for much of the half until a moment of inspiration from 20-year-old Tierney stirred the match into a life.
Manager Brendan Rodgers described Celtic's 3-0 away win over Anderlecht as "absolutely exceptional".
"To come away and get a 3-0 victory, and play that well after such a big game last weekend, really shows how the players have grown and are believing at this level".
Anderlecht paid their players £7.7million for qualifying for the Champions League, a win would see them shell out €1.5million of that windfall and €500,000 for a draw. I think Lenny was the last in 2012 and before that God knows when a Scottish team has won away from home.
It was was a hugely significant result for Celtic as they had failed to register a win in the group stages last season, the first under Rodgers.
Despite Celtic being strong domestically, their Champions League form has been poor and they were defeated 5-0 by PSG two weeks ago.
Now, pundit Ian Wright has told BBC Sport that whilst many will belittle Celtic, their result in Belgium was "very impressive", and manager Brendan Rodgers deserves major praise for the way he gets his side to raise their game in Europe after coasting through Scottish football.
"It takes experience and time and it takes belief".
"As a team then we were very, very good defensively".
Rodgers added: "I agree, Olivier didn't make a good start to the game".
The defender was released in behind by Olivier Ntcham's incisive pass and fed a ideal low cross from the left to the far post, where Griffiths was waiting to tap in the opener.
"After that Oli grew into it, he put his body on the line, got on the ball".