He equalled Tevita Vaikona's three try haul against South Africa in 2000.
The ex-Kangaroo also took his overall tally to six in his fourth match for his adopted country.
And Australia's Cup record 110-4 thumping of Russia in 2000 looked under threat when Tonga romped to a 38-0 half-time lead.
But Scotland dug deep in the second half, even getting on the board when halfback Danny Addy dived over from dummy half in the 62nd minute for the Bravehearts only points of the match.
However, winger Daniel Tupou completed his double as Tonga crossed for two tries in the final seven minutes to ensure the blowout.
Tonga's 46 point romp was just two short of their biggest Cup winning margin - 48 in their 66-18 rout of South Africa in 2000.
Taumalolo muscled over for a try of his own in the 17th minute, revelling in his new environment after controversially turning his back on New Zealand.
Tonga belied their world No.11 ranking, running amok in the first half with a side stacked with NRL stars including Andrew Fifita, Will Hopoate and Konrad Hurrell.
In contrast, the Bravehearts didn't live up to their world No.4 ranking after being depleted by pre-tournament injuries to key NRL players hooker Peter Wallace, fullback Lachlan Coote and centre Kane Linnett.
The game was played in quarters after the heat rule was evoked with humidity at times nudging 80 per cent.
Tonga will be expecting a tougher hit-out against Samoa in Hamilton on Saturday.
Scotland's misery may continue as they next play New Zealand at Christchurch on Saturday.
- AAP