The record comes four days after the Catalan club squandered a 4-1 first-leg advantage by losing 3-0 at Roma and failed to reach Europe's final four for the third year in a row.
Messi recently missed two international friendlies with Argentina because of a leg muscle problem, scored an 89th-minute equalizer in Barcelona's 2-2 draw with Sevilla.
Ronaldo netted twice and his partners in attack added a goal each to record a fourth straight win for Real Madrid in the Spanish league.
Raheem Sterling gave City lead inside a minute - he has now scored the earliest and latest goals in the league this season - before Christian Kabasele's own goal and a close-range finish from Sergio Aguero put City 3-1 up.
Ragnar Klavan headed home the winning goal at Turf Moor as Liverpool earned a hard-fought victory without three of its "Fab 4" attack, with Roberto Firmino demoted to the bench and both Philippe Coutinho and Mohamed Salah declared injured.
Failing to clinch their 19th straight victory, City could not equal the landmark set by Pep Guardiola's Bayern Munich in the 2013-14 season of the record winning streak in Europe's top five leagues.
By beating Swansea 4-0 on Wednesday, City racked up its 15th straight victory — a feat never achieved in the 129-year history of England's top division.
Lionel Messi and Luis Suarez took full advantage of the holes that opened up in the hosts' defence, scoring twice to give Barcelona a 2-0 win away from home that kept it five points ahead of second-place Valencia.
Basel joined United in the next phase from Group A by downing Benfica 2-0, whereas, Paris Saint-Germain won Group B despite losing to Bayern Munich 3-1, the second straight loss for the French league leader.
Manchester City has re-established its eight-point lead over second-place Manchester United thanks to their 12th straight league win.
Perth: The search for the missing Malaysia Airlines flight MH370 ended for the day Thursday with no sightings made in the search area in the southern Indian Ocean yet again and Australian Prime Minister Tony
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