- Oops!Something went wrong.Please try again later.
Messi scored both goals -- one with a header for only the fourth time in the competition -- as Barca beat Ajax 2-0 to equal Raul's record of 71 goals in the tournament on Wednesday.
"I am happy for Leo because of the work he does for the team. He is the number one, the best," said Barca midfielder Xavi Hernandez.
Bayern went through after a 2-0 victory at home to Roma, PSG saw off APOEL 1-0 while Porto beat Athletic Bilbao 2-0 with their goalscorers Colombian Jackson Martinez and Algerian Yacine Brahimi both taking their tallies to four in this season's competition.
Champions Real Madrid and Borussia Dortmund made sure of their last-16 places on Tuesday.
However, Chelsea missed a chance to also reach the knockout stages as they had to come from behind to snatch a 1-1 draw with minnows Maribor in Slovenia.
The 2012 winners, though, are in a far better state than English champions Manchester City whose mystifying failure to perform well in the competition continued as they had two men sent off in an embarrassing 2-1 home defeat to Russian outfit CSKA Moscow, who recorded their first ever win in England.
Their results rounded off a poor week for English clubs in the Champions League with Liverpool losing and Arsenal drawing 3-3 with Anderlecht, the Gunners having let a 3-0 lead slip in the final half hour on Tuesday.
Ukrainian side Shakhtar Donetsk also look certain to reach the last 16 after a 5-0 thrashing of Belarus champions BATE Borisov, Luiz Adriano adding to his five goals in the 7-0 win a fortnight ago with a hat-trick to move further clear in this season's overall scoring charts with nine.
Porto's fellow Portuguese side Sporting Lisbon are also in with a chance of reaching the next phase as they revived their campaign with a 4-2 home win over Schalke 04.
Sporting's Islam Slimani bookended the scoring, firstly putting through his own net to give the Germans the lead and then ensuring the hosts secured the points right at the end.
Barcelona still trail Paris Saint-Germain by a point at the top of Group F but the Spanish side's coach Luis Enrique was more relieved they had ended a run of two successive defeats and also avoided three consecutive away losses in the Champions League which last happened in 2005.
"The attitude of the team was marvellous against an opponent that had everything to play for," said Enrique.
PSG coach Laurent Blanc was content that his side did what was needed to secure their place in the last 16 -- Edinson Cavani scoring their fastest ever goal in the competition after just 57 seconds -- but is keener still to top the group.
"Now let's try to go on and finish first in the group because it gives you an advantage, a small one but an advantage all the same," said Blanc, whose side still have to travel to the Camp Nou to play Barcelona next month.
Bayern's victory against an under strength Roma starting line-up -- Gervinho and Francesco Totti started on the bench -- came at a price as impressive Austrian defender David Alaba, who created the first goal for Franck Ribery, suffered what appeared to be a serious knee ligament injury.
"We will miss him terribly," said Bayern coach Pep Guardiola.
"However, aside from that blow we are delighted to be in the knockout phase (for the seventh successive season) already, which is very important for the club.
"It also allows us to focus on the Bundesliga (they are four points clear of VfL Wolfsburg)."
City's reverse -- which saw Fernandinho and Yaya Toure sent off in the second-half -- left manager Manuel Pellegrini scratching his head for answers.
"It is a crisis of confidence and we must find out why by talking to the players every day and working together," said the Chilean handler.