Rizzo's RBI double ignited a three-run outburst in the second that gave Chicago an early lead, and his run-scoring single in the fourth capped a four-run rally that put the Cubs ahead 7-1.
Edwin Jackson (4-10) allowed three runs on seven hits over six innings to earn the decision, walking one and striking out six.
Hector Rondon put out the rally in despite allowing a wild pitch and a walk, and Kevin Gregg notched his 13th save with a 1-2-3 ninth.
Mariners starter Jeremy Bonderman (1-2) was tagged for six runs (four earned) on six hits in a 3 1/3-inning effort.
Jason Bay added a bases-empty homer for Seattle.