Alessandro Bastoni completed Inter Milan's late turnaround as they scored twice in the final six minutes to beat Parma 2-1 on Sunday, while Atalanta made it three wins in a row since the Serie A restart.
Gervinho gave Parma a first-half lead at the Stadio Ennio Tardini but Inter, who conceded a last-gasp equaliser at home to Sassuolo in midweek, fought back with headers from Stefan de Vrij and Bastoni to snatch a vital win.
Inter stay eight points adrift of leaders Juventus and four behind Lazio in second with 10 rounds of matches remaining.
"I thought it was a more than deserved victory. Thoroughly deserved," Inter assistant Cristian Stellini told Sky Sport Italia, with coach Antonio Conte forced to watch from the stands as he served a touchline ban.
Atalanta consolidated their grip on fourth place thanks to two stunning goals from Luis Muriel, who came on as a second-half substitute in their 3-2 victory at Udinese.
The Colombia international put his team back ahead with a magnificent 71st-minute free-kick, after Kevin Lasagna had levelled for Udinese in the 31st minute following Duvan Zapata's early opener for away side.
Muriel then put Atalanta two goals ahead with a superb volley that ensured Lasagna's second three minutes from time made no difference to the result.
Roma are facing another season without Champions League football after losing 2-0 at AC Milan.
Ante Rebic and Hakan Calhanoglu scored late to give Milan victory at a stifling San Siro to put Stefano Pioli's side three points away from the last Europa League place held by Napoli, who beat bottom side SPAL 3-1 in Naples.
Gennaro Gattuso's side, who have already won the Italian Cup this season, came out on top at the Stadio San Paolo thanks to goals from Dries Mertens, Jose Callejon and Amin Younes.
Roma stay fifth but are only three points ahead of Napoli and nine behind Atalanta in fourth, who are now clear favourites to qualify for Europe's top club competition.
Milan target Europe
Both teams started slowly but Milan dominated after the break with Rebic breaking through on 76 minutes, rifling the ball into the roof of the net at the third attempt after a frantic scramble following a Davide Zappacosta blunder.
Calhanoglu converted a penalty with a minute to go after Chris Smalling fouled Theo Hernandez in the area to earn a second win this week, despite the absence of star striker Zlatan Ibrahimovic with a calf problem.
"We were looking for a win against a strong opponent and we deserved to get it," said Pioli after their first win over one of the top-six sides this season.
"This victory gives us confidence to try to hit the goal of bringing Milan back to Europe.
"(Ibra) helped us raise our level. Let's not forget that we only lost one game with him.
"But the team is doing well without him and his return gives us other solutions."
Roma coach Paulo Fonseca conceded his side were struggling for fitness after the three-month coronavirus shutdown.
"They (Milan) were fresher in the second half," said Fonseca. "Let's not forget that they had seven days to prepare and it's their third game, it's not an excuse, it's the truth.
"I'm worried about physical fitness, we will play in two days."
Sampdoria sank further into the relegation mire after a 2-1 home defeat to Bologna which leaves them just a point above the drop zone, while Rogerio struck in the sixth minute of stoppage time to earn a 3-3 draw for Sassuolo against Hellas Verona.
Juventus beat Lecce 4-0 on Friday and Lazio came from behind to see off Fiorentina 2-1 on Saturday.