The world number six, who received a bye in the first round, broke the 2016 French Open quarter-finalist on five occasions to give herself some much-needed confidence on the Italian clay with the second grand slam of the year at Roland Garros starting next week.
The 25-year-old reached the third round in this event last year but has struggled on the clay surface this season, with a second-round exit at the Stuttgart Open last month coupled with a first-round defeat at the Madrid Open 10 days ago.
It was a slow start in the Rome heat with both players taking over 20 minutes to hold their opening two service games before Konta broke for the first time in the fifth game to take a 3-2 lead.
Konta needed over 12 minutes to hold in the sixth to extend her advantage to 4-2 and, after trading the next two games, the Briton eventually took the opening set with her fifth set point on Putintseva's serve in a hard-fought battle.
The British number one became more dominant against the agitated Putintseva and won the first three games of the second set - her fifth in succession - before Konta secured a double-break on the Kazakh's service to go 4-0 up.
Konta extended her winning run to seven games, despite being delayed for a few minutes after a ballboy suffered from heat exhaustion and picked up a time violation on her serve, before she broke Putintseva for the fifth time to seal a comfortable second set and be the first woman to advance to the third round.
The Briton will take on the winner of Lesia Tsurenko and Venus Williams, who play on Wednesday, for a place in the quarter-finals.
RESULTS FROM THE ITALIAN OPEN WOMEN'S SINGLES MATCHES
5-Johanna Konta (Britain) beat Yulia Putintseva (Kazakhstan) 6-3 6-0
Anastasija Sevastova (Latvia) beat Irina Begu (Romania) 6-4 6-4
Anett Kontaveit (Estonia) beat Andrea Petkovic (Germany) 6-3 6-4