City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat
Roma's captain Daniele De Rossi hit an unstoppable shot into his own net to break the deadlock in the 38th minute of what had been a delicately poised game and a second own goal 10 minutes into the second half, this time by Greek defender Kostas Manolas, stretched the runaway La Liga leaders' advantage.
Suarez effectively vanquished those hopes, however, by notching his side's fourth goal three minutes from time, scoring for the first time in the Champions League in over a year.
Roma had managed the game well until De Rossi's own goal and Dzeko could have won an early penalty when he was pushed over by Nelson Semedo and winger Diego Perotti failed to hit the target from a free header at the start of the second half.