It comes just three weeks after making his debut in the majors, and as Bazzana is yet to clear the 130 at-bat threshold that will see him graduate from rookie status, the Aussie moved up to number 13 on the MLB Pipeline Top 100 prospect rankings when it was updated this week.
Bazzana struck a 358-ft home run over right field with an exit velocity measured at 97.3mph (156kph).
The Guardians would go on to win the match 4-3, their sixth win in seven games following a successful series against the Los Angeles Angels and Cincinnati Reds.
At the time of completing his second career home run, Bazzana had a career batting average of .288 and an on-base percentage of .420, giving Guardians fans plenty to be excited about for the years to come.
He is on a single-year pre-arbitration rookie deal worth a reported US$780,000 (AU$1.1m).
Further improvement in his game could see him make a late-season case to end the Guardians' 36-year wait for a Rookie of the Year award, which last went to the franchise in 1990 when Sandy Alomar Jr hit nine home runs, 26 doubles and averaged .290 in his debut season as catcher.
"It's just been steady, ever since he got here," manager Stephen Vogt said of Bazzana recently after his maiden three-hit performance.
“Travis doesn't try to do too much. We know he's got pull-side power, but teams aren't challenging him in right now. They're pitching away, and if you keep doing what you're doing, you keep driving the ball the other way, guess what they have to do? They gotta start challenging you in."
"He's taking his walks, playing good defence. Good base-running."