The Argentinean put Mauricio Pochettino’s men ahead in the 16th minute with a left-footed effort following good work from Christian Eriksen and Roberto Soldado.
Former Spurs player Jermain Defoe then had a chance to equalise for the hosts but Brad Friedel was alert to the danger and came off his line to collect.
Toronto were made to pay when Lamela then doubled Spurs’ advantage in the 40th minute, rounding off a move he had begun himself.
Pochettino made 10 changes at half-time, while Toronto made seven, and the MLS side fought back.
Andrew Wiedeman scored in the 65th minute before youngster Jordan Hamilton equalised from close range.
But Andros Townsend curled home an effort into the top-right corner with five minutes remaining to earn Spurs’ first win of their tour, following Saturday’s 3-3 draw with Seattle Sounders.