Victor Wanyama had saved Celtic when he hit a decent opening from HJK Helsinki
Cetlic recovered from the loss of an away goal to take a first-leg lead against HJK Helsinki in Champions League qualifying round three.
Throughout the match, Kenya’s Victor Wanyama looked uncomfortable in the central defence as he played beside Mulgrew under the watch of Manchester United and Arsenal scouts.
Gary Hooper, James Forrest and Joe Ledley all had chances as the hosts started brightly.
But it was HJK's Rasmus Schuller who broke the deadlock with a close range volley just after half-time.
Hooper equalised with a tap-in before Charlie Mulgrew headed Celtic ahead in the tie.
Neil Lennon's men take on the Finns in next Wednesday's second leg at the Sonera Stadium.
In the third minute, Victor Wanyama had saved Celtic when he hit a decent opening from HJK Helsinki. He went on to create a chance when he dazzlingly controlled the ball with his chest down for Ledley who punched a low shot towards the bottom corner.
The Scottish Premier League champions threatened from the off with Georgios Samaras heading a long ball onto Hooper only for the angle to get the better of the striker.
Samaras was prominent again with a cross towards James Forrest, who headed wide before indicating his displeasure at Mikko Sumusalo's aerial challenge in the six-yard box.
Hooper and Kris Commons failed to connect properly with Forrest's cutback and Ledley flashed a shot wide from the loose ball before testing goalkeeper Ville Wallen with a controlled volley moments later.
HJK weathered the storm and Joel Perovuo forced Celtic keeper Fraser Forster into a save with a low 25-yard drive.
And the Finns dealt a blow to Celtic's hopes when a neat passing move put Schuller through on goal shortly after the break.