A rout appeared to be on the cards after hooker Julián Montoya's hat trick of tries and one from winger Santiago Carreras — all converted by fly-half Benjamin Urdapilleta and all before Tonga has scored a point.
Instead, Tonga rallied with two fine tries from fullback Telusa Veainu, who looked sharp on his return from a nagging foot injury.
This was a comfortable win, and finally snapped a 10-game losing streak, but the way Tonga got back into the game and pushed hard for a third try concerned Ledesma.
These might prove the easiest tries he'll get, such was Tonga's poor defending early on. Carreras was also a new pick on the left wing, and the 21-year-old got his first international try.
It all seemed so easy at this point, with not even 30 minutes played.
"Just errors, poor skill, bit of miscommunication. Typical Tier Two errors," said Tonga coach Toutai Kefu, who won the 1999 World Cup as a player for Australia. "You can't let Tier One teams get ahead like that. But I'm proud of how the boys fronted up physically."
But Tonga woke up with a well-taken try from Veainu — a neat side-step into the left corner from the Leicester Tigers favorite.
"He offers us an X-factor out wide," Kefu said. "It's great to have him back. Having a player of his caliber and class is fantastic for us."
Flanker Tomas Lavanini prevented a second Tonga try on the half-time buzzer, barging winger David Halaifonua out of bounds in the left corner. The try was ruled out, although there were questions over the tackle.
"I thought it was a shoulder charge. If we would have got that (try) we would have come out in the second half with a lot more belief and confidence," Kefu said. "There were a couple of 50-50 (decisions) today we didn't get."
After the break, the pace of the contest dropped at a humid 22,000-capacity Hanazono Rugby Stadium.
Argentine scrumhalf Tomas Cubelli had a try ruled out in the 52nd minute for a knock-on, following a referral to the television match official.