Newsome had a 10-yard, spinning rushing touchdown midway through the second quarter and Bryant Shirreffs’ 32-yard pass to Tyraiq Beals set up Johnson’s 2-yard touchdown with 7:10 left in the third quarter that gave UConn a 19-10 lead.
Shirreffs threw for 270 yards and ran for 40 for the Huskies, who are off to a 2-0 start for the first time since 2008.
Newsome ran for 73 yards on 13 carries and Johnson had 39 yards on 18 attempts.
The Black Knights (0-2) ran for 180 yards, 129 by quarterback Ahmad Bradshaw.
Bradshaw ran for a 56-yard touchdown in the second quarter that gave Army a 10-3 lead, but the Huskies scored 19 unanswered points.
Army drew within five points when A.J. Schurr threw a 71-yard touchdown pass to Joe Walker with 4:51 remaining.
UConn’s Andrew Adams intercepted Schurr’s pass with 2:21 to play to seal the victory.
Bobby Puyol kicked three field goals, including two in first half to give UConn a 12-10 lead heading to the locker room.
UConn plays No. 21 Missouri on Sept. 19 at noon in its first road game of the season.