Activists from climate group Ultima Generazione (Last Generation) burst onto the Pietrangeli court, where American Madison Keys was leading Sorana Cirstea 6-2, 3-1 in the women's last 16.
Wearing orange vests, they threw a liquid onto the court and confetti before being removed by security staff.
After a half-hour stoppage to clean the court, Keys to complete her win over Romania's Cirstea 6-2, 6-1 and set up a potential quarter-final clash with world number one Iga Swiatek.
"Honestly, as soon as I saw them come over the barrier my first thought was 'should I go tackle them?'," joked Keys to reporters.
"Unfortunately it's starting to become a little bit of a common thing that's happening so at that point I figured it as going to be a little bit of a delay and just tried to get off the court and regroup."
Two people also burst onto an adjacent court 12, where a men's doubles match was underway and also threw a liquid and confetti.
The stands were evacuated as organisers awaited the arrival of police as, according to a spokesman for the tournament, at least one person had tried to glue their feet to the floor of the stands in order to slow their removal.
Play also resumed later in the doubles match.
"Obviously it's not the greatest feeling when you're on court, you first reaction is kind of your own safety. I think maybe banning cementing glue from bags would be a start," added Keys.
"It's obviously something that's becoming more of an occurrence and something that tournaments are going to have to figure out how to stop."
In March three Ultima Generazione activists briefly interrupted the Rome marathon before being arrested by police.
The group demands the Italian state create a reparations fund of 20 billion euros ($22 billion) for "all people suffering damage due to climate change".
In recent months their activists have thrown soup, cakes and paint on cultural sites and artworks in museums in shock tactics to spread their message.
Scientists say climate change induced by human activity is increasing the intensity, frequency and length of extreme weather events such as droughts, heatwaves and wildfires.
