The 22-year-old Janowicz improved his record against top-10 opponents to 3-5, having closed last year by reaching the Paris Masters final as a qualifier, beating Andy Murray and Janko Tipsarevic along the way. The 24th-ranked Janowicz is one of only five players under the age of 24 in the top 40.
After beating Tsonga with a forehand passing shot up the line on match point, Janowicz celebrated by ripping his shirt apart.
Last week's Madrid Open runner-up Stanislas Wawrinka withdrew before his match against Alexander Dologopolov with a right leg injury.
Later, Rafael Nadal begins his bid for a seventh Rome title against Fabio Fognini of Italy.