Roma saw off relegation-threatened Spal 3-0 in Serie A on Saturday and stayed confident for the trip to Liverpool for the first leg of the Champions League semifinals.
Bottom side Benevento was 12 points from avoiding the drop after stunning AC Milan 1-0 and, with four rounds remaining, could still mathematically achieve safety.
While trying to win the Champions League, Roma is also trying to secure qualification for next season, and moved three points above fourth-placed Lazio, which hosts Sampdoria on Sunday.
The top four teams from Serie A qualify for the Champions League.
"We had the right attitude and it wasn't easy to come here and have this kind of match," Roma coach Eusebio Di Francesco said. "The guys' performance really pleased me, we were very mentally aware.
"If I had to highlight something that I didn't like it was that we wasted a lot of chances.We have to be more clinical, starting in Liverpool."
Di Francesco rested key players for Tuesday's match, including Alessandro Florenzi, Edin Dzeko and Cengiz Under.
It took half an hour for Roma to break the deadlock when Francesco Vicari turned Lorenzo Pellegrini's cross into his own net as he tried to prevent a Kevin Strootman tap-in.
Radja Nainggolan doubled Roma's lead six minutes into the second half after a free kick was cleared only to the edge of the area.
Shortly after, Patrik Schick headed in Pellegrini's cross for his first league goal for the capital club.
Spal lost for the first time since Feb. 18 — a run of two wins and six draws — and was just one point above the relegation zone.
Benevento knew it needed to win at Milan to avoid certain relegation.
The last time the sides met, Benevento goalkeeper Alberto Brignoli sensationally headed in a stoppage-time equalizer to secure his side its first ever Serie A point in a 2-2 draw.
Saturday's result was its first Serie A away win.
"We put our pride on the pitch," Benevento goalkeeper Christian Puggioni said. "What happened was an advertisement for football: Even the last team in the standings, practically doomed, can come here and impose their own game."
Benevento took a shock lead at San Siro in the 29th minute when Nicolas Viola's throughball sent Pietro Iemmello clear and he slotted past Gianluigi Donnarumma.
Benevento endured the last 10 minutes with 10 men after forward Cheick Diabate was sent off following a second yellow card.
"The team is regressing: When you play without spirit you make these embarrassing shows of yourself," Milan coach Gennaro Gattuso said. "I'm the first one who is responsible.
"We have to change: You can't play without desire, without competitive anger. That's where the regression lies: We are a team which creates chances but we seem to have little desire to hurt our opponents. We have to apologize to our fans and the first to do so is me."
Fiorentina surprisingly fell at Sassuolo 1-0 after playing an hour with 10 men.
Midifielder Bryan Dabo was sent off for a second booking, tugging back Domenico Berardi on the half hour after being shown a first yellow card for a foul on Simone Missiroli in the sixth minute.
A second successive win for Sassuolo all but guaranteed it safety, nine points clear of the drop zone.
Fiorentina remained three points behind AC Milan in the race for the final Europa League spot.