The American veteran made a strong start against the 16th seed, claiming successive breaks as Janowicz managed to win just four of his opening 12 points on serve.
Blake quickly claimed the first set 6-1 in 27 minutes, winning 83% of his points on first serve.
Janowicz continued to struggle on serve early in the second set but hung tough, saving five break points to keep the match alive.
With the second set finely poised at 4-5 Janowicz earned two set points on his opponent's serve, but was unable to make either chance count as Blake sent a pair of winners down the line.
The 33-year-old then found form at the baseline to seize control, scorching his 30th winner down the line at match point to wrap up a 6-1 7-5 success.