Willson Contreras also went deep for the Cubs. Nick Madrigal had three hits and Nico Hoerner drove in two runs.
Suzuki is batting .400 and has hit safely in eight straight games with an at-bat. The outfielder from Japan has reached base in all nine games to begin his Cubs career.
Rowan Wick won in relief and David Robertson earned his third save.
Ryan McMahon homered for the Rockies.
The Cubs roughed up Colorado starter Austin Gomber for five runs -- four earned -- in 4 1/3 innings.