The bonus-point win in Leicester lifts the Pumas above Tonga to second place in Pool C, with the Pacific Islanders yet to play group leaders and defending champions New Zealand while Argentina face lowly Namibia as they look to seal passage into the last eight.
Tongan centre Siale Piutau had said the Pacific Islanders' "wolf pack mentality" would hound the Pumas into submission, and they certainly gave as good as they got in a free-flowing first half to trail 20-13 at the break, with two tries apiece.
"It was not the match we had dreamt of," Argentina captain Agustin Creevy said. "We made mistakes in defence, in attack there were clear examples of tries we should have scored and didn't. Luckily it happened in a match we won and we can correct them."
Ultimately, playmaker Sanchez proved the difference, tormenting Tonga with the boot and with ball in hand, weighing in with 25 points from a try, four conversions and four penalties.
Tonga contributed to an exciting first test meeting between the two teams and drew first blood with a try from flyhalf Kurt Morath, but Argentina hit back with a pair of tries to take a lead they would never relinquish.
The first arrived when prop Ramiro Herrera broke free to feed fullback Joaquin Tuculet for a try under the posts. Nippy Santiago Cordero then fielded the deep restart to launch a sidestepping counter-attack to set up a try for wing Juan Imhoff.
Tongan tenacity was rewarded with a stunning try on the stroke of halftime; a fine attacking move across the pitch ending with wing Telusa Veainu offloading for marauding prop Soane Tonga'uiha to dive over.
Their challenge faded in the second period and Morath's two successful penalties were a poor return from his six shots at goal.
Sanchez, meanwhile, continued to nail his kicks and added his try before replacement forward Julian Montoya went over in the corner to secure the bonus point and right wing Cordero closed out the match with the fifth try.
Tonga captain Nili Latu said they had let themselves down with individual errors and rued the missed kicks that could have kept Argentina under pressure.
“What let us down today was our lack of composure when they had the ball,” he said.
“At halftime, we wanted to get points. The momentum was on our side but mistakes crept in. We missed four kicks today."
(Editing by David Goodman)
