Liverpool and Chelsea both earned 1-0 wins in the Champions League, to give them great chances of going through.
Chelsea beat Italian side Juventus at Stamford Bridge, but it was Liverpool's 1-0 win away to top Spanish side Real Madrid that was the big news.
Yossi Benayoun headed in the winner for the Reds in Madrid, and Liverpool looked very solid in defence too.
The only bad news came when star striker Fernando Torres had to go off with an ankle injury.
Chelsea made a brilliant start to their match against Juventus, opening the scoring after only 13 minutes.
ENGLISH CLUBS IN THE CHAMPIONS LEAGUE - FIRST LEG SCORES
Inter Milan 0-0 Manchester United
Arsenal 1-0 Roma
Real Madrid 0-1 Liverpool
Chelsea 1-0 Juventus
That goal came from Didier Drogba, who scored his first goal of 2009 thanks to a great pass from Salomon Kalou.
But Juventus played pretty well too and were perhaps a little unlucky not to be taking an away goal back to Turin for the second leg.
Both Liverpool and Chelsea play the second legs of their ties on Tuesday 10 March.