Roma winger Cengiz Under sent the ball over the bar from point-blank range with goalkeeper Thibaut Courtois already down on the ground in first-half added time and two defensive blunders led to Gareth Bale's goal immediately after the break.
Lucas Vazquez then added another for Madrid against a demoralized Roma.
Both three-time defending champion Madrid and last season's semifinalist Roma had secured spots in the last 16 before kickoff, as Viktoria Plzen won 2-1 at CSKA Moscow in the other group match earlier to send them through.
Madrid, which is assured of winning the group, leads with 12 points, Roma has nine, and Plzen and CSKA four each.
The victory offered some welcome relief for new Madrid manager Santiago Solari, who was facing pressure following a 3-0 loss at Eibar in the Spanish league in his first match since being given the job permanently.
Solari was asked if Madrid, a record 13-time European champion, remained the favorite to win the competition.
"That's always the case, due to our history over the last 115 years," Solari said. "Real Madrid is the favorite until another squad wins more."
Roma coach Eusebio Di Francesco, meanwhile, remains at risk after a loss at relegation-threatened Udinese at the weekend and with a home match against Inter Milan following the Madrid defeat.
"We were missing many important players and we put out a very young team tonight but we went out with a positive attitude," Di Francesco said. "But every time we concede a goal we completely fall apart. That's the thing that makes me angriest, because it's something we had discussed."
Roma dominated the first half but wasted a series of excellent chances, none greater than Under's opportunity which practically came on a silver platter from Nicolo Zaniolo's cross.
The error left the 21-year-old Under holding his head in frustration and the Turkey international had to be consoled by Alessandro Florenzi, who was Roma's captain in absence of the injured Daniele De Rossi.
"In the first half, we were superior to Real Madrid — a side that won the Champions League three straight years. But if you are superior and don't take advantage of your chances, you're going to lose," Roma defender Kostas Manolas said.
Roma also protested for a penalty early on when Dani Carvajal appeared to handle the ball at the edge of the area. But the referee signaled to play on.
Roma sorely missed injured striker Edin Dzeko, who along with Lionel Messi is the joint top scorer in the Champions League with five goals.
With Roma fans at the filled Stadio Olimpico still fuming over Under's miss, the frustration turned to rage when Madrid scored on its first chance of the second half.
A poor clearance by Roma goalkeeper Robin Olsen was headed back by Roma defender Federico Fazio directly to Bale, who scored easily.
Then near the hour mark, Vazquez tapped in after a headed pass from Bale.
Before the match, retired captain Francesco Totti was inducted into Roma's hall of fame during a ceremony that retired Madrid greats Raul and Roberto Carlos also took part in.