Bryant clubbed a grand slam off a position player to cap a seven-run ninth inning, while Denorfia hit a three-run shot and an RBI double.
Tsuyoshi Wada (1-1) and Yoervis Medina combined on a four-hit shutout. Wada scattered four singles over seven innings with two walks and six strikeouts.
Murphy relieved Raburn with two men aboard and got a popup from David Ross that appeared to be the final out of the inning.
Francisco Lindor, though, lost the ball and it dropped in for an error.
Addison Russell then hit an RBI single and Murphy hit Mike Baxter with the bases loaded before Bryant homered to center field.
Kyle Schwarber, the latest of the Cubs' prized prospects to join the club, sparked a six-run second inning with his first MLB hit, an RBI triple into the right-field corner off starter Shaun Marcum (3-2).
The fourth overall pick in last year's draft, Schwarber finished 4-for-5, scored three runs and had two RBI.
Chicago ended up hitting for the cycle in the second against Marcum. Denorfia doubled home Schwarber and Russell and Anthony Rizzo each blasted two-run homers.
Nick Hagadone replaced Marcum to begin the third and gave up three straight singles, including a run-scoring hit by Schwarber.
Francona then pulled Hagadone from the game after he fell behind 2-0 to Denorfia. Ryan Webb inherited the count and yielded the drive by Denorfia.
The Cubs had a season-high 18 hits ... Rizzo snapped an 0-for-20 slump with his second-inning home run ... Bryant extended his hitting streak to 13 games ... Cleveland second baseman Jason Kipnis has now hit safely in 21 straight home games, the second-longest streak all-time at Progressive Field ... Marcum allowed two hits and struck out five without a walk in seven innings of a 6-0 win over Seattle last Thursday.