Wednesday night's win was the Red Sox's first World Series win at Fenway Park in nearly 100 years, the Boston Herald reported.
"BPD thanks the tens of thousands of great @RedSox fans who showed Boston pride & celebrated responsibly #WorldSeriesChampions!!" the Boston Police Department tweeted early Thursday.
Hub and transit police arrested a total of 10 people, all for unruly behavior.
Police arrested 15 people at a celebration at the University of Massachusetts Amherst, 14 of whom were students.
About 3,000 students gathered in the southwest residential area at the University of Massachusetts Amherst campus to celebrate Wednesday night's win, WGGB-TV, Springfield, Mass., reported. Some members of the crowd became unruly, throwing liquor bottles and toilet paper, and climbing trees, WGGB said.
A UMass Amherst spokesman said in a statement, "The crowd, which grew steadily during the contest, was calm until the end of the game." With the help of the Amherst Police Department and state police, the school was able to disperse the crowd in "less than an hour."
Two people were charged with assault and battery on a police officer, while most of the others were arrested for failing to disperse, the school said.
Meanwhile, five students were arrested at the University of New Hampshire and charged with disorderly conduct.
Thousands of students gathered on Main Street near the school, lighting off fireworks and throwing bottles and liquid at police, WMUR-TV, Manchester, N.H., reported Thursday.
The crowd was dispersed by pepper spray and pepper bullets, campus officials said.
At Plymouth State University, students set small fires on campus and some ran naked through the campus, WGGB said. One person climbed a light pole and shook it until it toppled.
At Keane State College, students threw glass bottles, rocks and ice at officers and other students, police said. The crowd also flipped another student's car over.
"The crowd of students became belligerent and destructive, attempting to damage property on the campus," said Keene police Lt. Todd Lawrence.
No arrests were reported at Plymouth or Keane.