David Luiz's goal was Brazil's second of the night after Thiago Silva had given them an early lead against Colombia.
James Rodriguez pulled a goal back for the Colombians after Julio Cesar had conceded a late penalty, but Luiz and his team-mates held out for a famous win as the World Cup's host nation reached the last four and kept their hopes of winning the tournament alive.
While Silva opened the scoring with a close-range strike from a corner, former Chelsea man Luiz scored from a long-distance free kick - it was one of goals of the tournament.
And Hazard, who is yet to play his World Cup quarter-final for Belgium against Argentina, was quick to congratulate the 27-year-old on social networking site Instagram.
Eden hazard (@hazardeden10) July 4, 2014
Hazard also tagged Brazil's Chelsea contingent - Oscar, Willian and Ramires.
Luiz is no longer a Blue, of course, having joined Paris Saint-Germain for a reported £50 million this summer, though he worked with 23-year-old Hazard for two seasons at Stamford Bridge.
The pair could still meet in the final, should Brazil defeat Germany in the semi-finals and Belgium win their next two clashes to book a place in the showdown at the Maracana.