Schewinsteiger split a pair of defenders and, from just beyond the top-left corner of the 6-yard box, side-netted a low finish for Chicago (3-1-2) to open the scoring moments before halftime.
Nikolic made it 2-0 early in the second half, poking Luis Solignac's deflected entry past Cody Cropper from point-blank range, and capped the scoring in the 73rd minute. Schweinsteiger fed David Accam, streaking down the left sideline, who placed perfectly a cross to the spot where Nikolic tapped it into the net.
New England (2-3-1) played most of the match a man down after Je-Vaughn Watson was sent off in the 27th after receiving a pair of yellow cards just minutes apart. The Revolution had just four total shots and had a three-game unbeaten streak snapped.