He took to the court after a 90-minute delay but proved too good for world number 73 Ivashka once the match began as he blasted 26 winners and converted three of his six breakpoint chances to set up a meeting with Grigor Dimitrov (31).
"I was ready for it. I'm playing well. It was a good first match and I'm really happy to get through again," Wawrinka said. "I have been working hard to get to this level.
"This year I'm playing much better, but I need to win more matches.
"That's what I'm missing a bit, the confidence to win more matches. But in general the level is great."
Joining the three-times Grand Slam champion in the next round was Tomas Martin Etcheverry (23), who downed Luca Van Assche (18) 7-6(7) 6-3 to earn a meeting with Novak Djokovic (35).
Former world number one Andy Murray (35) will take on Italian wild card Fabio Fognini (35) later in the evening as he continues his preparations for the French Open starting later this month.
STEPHENS CRUISES
In the women's tournament, former US Open champion Sloane Stephens (30) beat Nadia Podoroska (26) 6-4 6-1 to open her Rome campaign in style following her triumph in Saint Malo last week.
Up next for the American is two-time major champion Victoria Azarenka (33).
Lesia Tsurenko (33) overcame two-time champion Elina Svitolina (28) 6-4 6-3 in an all-Ukrainian clash, the latter having returned to the WTA tour at the Charleston Open last month following her maternity break.
Colombia's Camila Osorio (21) battled from 5-2 down in the last set and saved three match points to defeat Varvara Gracheva (22) 7-6(4) 1-6 7-6(4), while Anastasia Pavlyuchenkova (31) beat Sara Errani (36) 6-1 6-1 to set up a meeting with the top-ranked Iga Swiatek (21).
