Three Tonga players had already been sin-binned when Solomon Haumono and Joe Foliaki saw red after the mass brawl.
First-half scores from Rob Purdham, Brett Ferres and Mark Calderwood helped England to an 18-10 half-time lead.
The greasy conditions at the Halton Stadium put a premium on looking after the ball in the collision and Tonga paid an early price for their failure to do so.
Purdham opened the scoring on 12 minutes after good work from Lee Radford, Ashley Gibson and Hodgson gave him the opportunity.
Ferres pounced on a loose ball at the end of a prolonged spell of pressure to score England's second try.
Taniela Tuiaki cut the gap, powering through three tackles to cross on the right and Etuate Uaisele was unlucky to have his touchdown ruled out for a knock-on while contesting the high ball.
A fight broke out after a tackle involving Ferres and Makasini Richter, and when things simmered down both players were sent to the sin-bin.
But moments later, Mateo - with blood still streaming from his nose as a result of the fight - scored a superb try, collecting a return pass from Willie Tupou after putting the loose forward through the hole.
Shortly before the break, Calderwood was able to stroll over on the left, the beneficiary of a superb Nick Scruton break.
Tonga's heads did not drop, though, and they scored the first points of the second half through Tyrone Smith's try.
The score buoyed Tonga and, after forcing a repeat set, it took a breath-taking tackle from Lee Smith to stop Mateo just short of the line.
England finally began to draw clear through Hodgson's try on 62 minutes, the winger cutting inside several tackles to dive over.
With Eorl Crabtree starting to run riot, England began to turn the screw and the pressure eventually resulted in a sin-binning for Samuela Moa.
England made sure of the win through Jamie Rooney's 69th-minute try, after a break from the outstanding Calderwood.
With the match out of their reach, Tonga lost the plot with a string of penalties coming about as a result of swinging arms and high tackles, and they had Lopini Paea yellow-carded.
And with time running out, the biggest fight of the match broke out.
Referee Richard Silverwood took several minutes to bring it under control and when he did Haumono, who had joined in from the side of the pitch where he was waiting to come on as a substitute, and Foliaki were sent off.
England coach Paul Cullen said: "I can't remember the last time I won any silverware. It's been a tough month's work but these young English players have got an awful lot out of it.
"And, if the Tongans hadn't kicked up in the last five minutes, they would have got something out of this competition as well.
"I have been impressed by the way they have gone about their business apart from that nonsense at the end."
Tonga coach Jim Dymock said: "The boys are very proud people. They love their country and just wanted to win. A couple of things didn't go our way and they got frustrated.
"I think they were just standing up for themselves. That's Test-match football, isn't it? That's what it's about, putting your heart and soul into your jumper.
"They might have gone a little overboard but nothing that you haven't seen in the Tri-Nations.
"I think a lot of it was push and shove and hopefully it will be swept under the carpet."
England: (18) 32 Tries: Hodgson, Ferres, Calderwood, Hodgson, Rooney Goals: Rooney 6
Tonga: (10) 14 Tries: Tuiaki, Mateo, Smith Goals: Mateo
England: Ashton, Hodgson, Atkins, Purdham, Calderwood, Cooke, Rooney, Bailey, Gibson, Crabtree, Radford, Jones-Buchanan, Ferres. Replacements: Smith, Dowes, Horne, Scruton.
Tonga: F. Talanoa, Waisele, Tuiaki, L. Paea, Richter, Mateo, Smith, Haumono, Uasi, Moimoi, L. Paea, Fa'aoso, Tupou. Replacements: M. Paea, Taufa'ao, Foliaki, Falamaki.
Referee: R Silverwood (Dewsbury)