Ollie Watkins scored twice as Aston Villa beat Bologna 3-1 in their Europa League quarter-final, first leg on Thursday, while Nottingham Forest held Porto 1-1 thanks to a comical own goal from Martim Fernandes.
Freiburg also have one foot in the last four after beating Celta Vigo 3-0.
Villa boss Unai Emery is aiming to win the competition for a fifth time and the favourites rode their luck to emerge victorious in Italy.
"It could've been different," said Watkins. "We got lucky."
Bologna made a bright start to their first European quarterfinal in 27 years.
An Ezri Konsa own goal was ruled out by a VAR review for a marginal offside against Santiago Castro before Lewis Ferguson hit the bar.
But the Coppa Italia winners were undone by some awful set-piece defending to allow Villa two of their goals.
Konsa headed into an unguarded net just before the break after Federico Ravaglia flapped at a corner.
Watkins quickly doubled the visitors' advantage after half time with a cool finish after Emi Buendia won possession deep in Bologna territory.
Federico Bernardeschi hit the post and Jonathan Rowe was denied by a brilliant Emi Martinez save.
Rowe's stunning finish in the 90th minute looked to have given Bologna a foothold in the tie.
But Watkins was left completely unmarked to tap in from a corner deep into stoppage time and further his case for inclusion in England's World Cup squad.
"Back end of the season I'm raring to go," added Watkins. "I'm excited for the next few games. I'm hungry."
FREIBURG'S RECORD RUN
Villa will face the winners of the tie between Porto and Forest should they progress to the semifinals.
An all-English affair in the last four is on the cards after Forest were handed a gift by Fernandes.
Porto capitalised on a strong start when William Gomes turned in at the far post.
But the lead lasted barely two minutes before Fernandes found his own net from just inside the Porto half as he overhit a pass back to goalkeeper Diogo Costa.
Forest striker Igor Jesus had a goal ruled out in the second half, but the visitors were happier with the draw that leaves the tie up for grabs next week at the City Ground.
"It was a good result," said Forest boss Vitor Pereira.
"At 1-1 at half-time in the tie, it's open, and we're at home to decide who qualifies."
The best European run in Freiburg's history looks set to continue after Celta were blown away by the Bundesliga side.
Vincenzo Grifo's curling effort gave the home side the perfect start on 10 minutes.
Niklas Beste doubled Freiburg's lead at the end of a fine team move and Matthias Ginter headed in 12 minutes from time to secure a commanding first leg lead.
Braga and Real Betis drew 1-1 in the other quarterfinal, first leg on Wednesday.