The Catalans and Bayern Munich both secured their places in the knockout draw and demonstrated once again why they are surely the best teams in Europe just now, with Bayern Munich crushing Olympiakos 4-0 at the Allianz Arena.
Barcelona discovered they had qualified from Group E before they had even kicked a ball at the Camp Nou, the 1-1 draw between BATE Borisov and Bayer Leverkusen in Belarus ensuring their passage.
Dani Alves set up Suarez to tap in the opener before Messi, captaining the side in his first start since returning from injury, made it two at the end of a superb move involving Neymar and Suarez.
Suarez struck again just before the interval with a sweet volley and the rout continued in the second half as Neymar, Suarez and Messi all combined to give Gerard Pique a tap-in.
Also Read
Roma's misery was compounded when Edin Dzeko had a late penalty saved by Marc Andre ter Stegen, although Dzeko did pull one back with the last kick of the game.
BATE opened the scoring in the second minute in Belarus when a Mikhail Gordeichuk shot squirmed under Bernd Leno in the away goal, but Admir Mehmedi equalised in the second half.
Roma still have their destiny in their own hands, though -- a win at home to BATE next month will see them finish second.
Holger Badstuber was sent off early in the second half on
his return after his latest lengthy lay-off but Kingsley Coman added a fourth.
While that win saw Bayern secure top spot in Group F, Arsenal kept their hopes alive by beating Dinamo Zagreb 3-0 at the Emirates Stadium.
Mesut Ozil headed the Premier League side ahead and Alexis Sanchez added a brace, meaning the Gunners can still qualify for the last 16, provided they win at Olympiakos next month by at least a two-goal margin or by winning by a one-goal margin having scored three or more goals.
The other game in Group G saw Dynamo Kiev win 2-0 at Porto with Andriy Yarmolenko netting a first-half penalty before Derlis Gonzalez wrapped up the win.
Just two points separate Chelsea, Porto and Dynamo Kiev but Jose Mourinho's side need only draw at home to the Portuguese club next month to go through.
"Very important, especially with what happened in Porto we really needed to win this match, and also important to get two victories in a few days," Mourinho told BT Sport.
Elsewhere, Zenit St Petersburg, who had already qualified for the last 16, made it five wins out of five in Group H by beating Valencia 2-0 in Russia.
Oleg Shatov and Artem Dzyuba scored in each half before Valencia defender Ruben Vezo was sent off.
Gent leapfrogged Valencia into second with a 2-1 victory away to Lyon that eliminated the French team from all European competition.
Jordan Ferri had put Lyon ahead but Danijel Milicevic levelled with a free-kick before Kalifa Coulibaly's last-gasp winner.
Real Madrid and Manchester City, who play on Wednesday, had already secured their places in the knockout stage.