Spurs raced into a 2-0 lead thanks to efforts from frontmen Harry Kane and Soldado in the fourth and 11th minutes respectively.
Jamie Lindsay pulled a goal back for Celtic in the 43rd, but a minute later Lewis Holtby restored the two-goal cushion and Tottenham kept the momentum going after the break.
Midfielder Lamela - who, like Soldado, is looking to bounce back after a disappointing first season with the London club - made it 4-1 just before the hour mark.
And a Christian Eriksen free-kick and Emmanuel Adebayor penalty wrapped up the rout in the last 10 minutes, while Celtic's misery was compounded by a red card for Efe Ambrose - his second this week, having been dismissed in Wednesday's Champions League qualifier against Legia Warsaw.
Newcastle, playing at Schalke's Veltins Arena, conceded three goals in 18 first-half minutes en route to a 3-1 loss to Spanish side Malaga.
Sergi Darder opened the scoring in the 25th minute with a long-range strike that went in off the woodwork.
Samu Castillejo volleyed in at the far post in the 32nd minute and the same man then netted a deflected effort towards the end of the half before Gabriel Obertan fired in a consolation on the hour.
Summer signing Bafetimbi Gomis was on the scoresheet for Swansea as they beat Reading 3-1 at the Madejski Stadium.
The France striker provided a cool finish to seal the victory in the second half. Wayne Routledge had earlier - after Wilfried Bony crashed a penalty against the crossbar - scored twice in three minutes to put the Swans in charge, with the hosts replying through a Nick Blackman wonderstrike.
Crystal Palace suffered a 3-2 defeat at Championship newcomers Brentford.
A flurry of goals early in the second half saw Jonathan Douglas and Andre Gray put the home team 2-0 up and Palace then draw level through Glenn Murray and Marouane Chamakh. Moses Odubajo subsequently notched the winner.
A Stoke XI drew 0-0 at Burton and West Brom went down 1-0 at Nottingham Forest courtesy of a Matty Fryatt goal.
Charlie Austin and Junior Hoilett scored a brace apiece in QPR's 4-0 win at Shamrock Rovers, while summer recruit Marvin Sordell's effort steered Burnley to a 1-0 triumph at Blackpool.
Leicester drew 1-1 at Preston, with Liam Moore's goal cancelled out by a Tom Clarke header.