Aliseda's fourth tally of the season came on a right-footed shot from the right side of the box off an assist from Brian Gutierrez to beat Revolution goalkeeper Matt Turner into the bottom left corner.
Gustavo Bou's chip shot in the 76th minute had put the Revolution ahead 2-1. It was Bou's team-leading 14th goal of the season and came on Revs captain and midfielder Carles Gil's MLS-leading 17th assist of the campaign.
Alvaro Medran also had a goal in the 49th minute and Gabriel Slonina stopped six shots for Chicago (7-16-7, 28 points), which improved to 1-11-2 on the road this season. The Fire had dropped four consecutive road matches and are 1-17-7 on the road since the start of last season.
Chicago earned draws in two of its three matches with New England this season after a 2-2 tie at home on April 17 and a 3-2 home loss on Sept. 22.
Rookie midfielder Wilfrid Kaptoum scored his first MLS goal in the 47th minute for the Revolution (20-4-6, 66 points). Turner finished with three saves for New England, which was denied its club record-tying 12th home win while falling to 11-1-3 at home.
With the tie, the Revolution moved within six points of LAFC's single-season MLS record of 72 points set during the 2019 season.
Chicago visits FC Cincinnati on Wednesday to complete its three-game road trip. New England opens a two-game road swing at D.C. United on Wednesday before back-to-back matches at home to close out the regular season.