Barca met seven-times winners AC Milan at the Nou Camp but the stock of the faltering Italians has fallen so much that even an average display from the hosts sealed a 3-1 success in Group H, Lionel Messi scoring a penalty and a cheeky third.
Miranda grabbed Atletico's opener after 11 minutes before Raul Garcia rose athletically to head home the second, with Filipe Luis making it three for this term's potential surprise packages on halftime.
Diego Costa missed a penalty but added a fourth goal on 82 minutes as Diego Simeone's men made sure of top spot and equalled their biggest Champions League win in reaching the knockout stages for the first time since 2008/09.
"We knew it was very important to win today because of the result between Zenit and Porto. The team was great today and we deserved to reach the round of 16," the forward told reporters.
Zenit St Petersburg stayed as favourites to take second place and qualify after Hulk scored the equaliser but also missed a spot kick in a 1-1 home draw with his former side Porto.
Arsenal grabbed swift revenge for last month's home loss to Dortmund by snatching a 1-0 win at last term's runners-up, Ramsey's 62nd-minute header the latest in his purple patch of goals to leave Juergen Klopp's third-placed side suddenly fretting.
Wales midfielder Ramsey, castigated by many Arsenal fans last season for a series of toothless displays, netted his 11th goal of the season when he nodded in after good work by Mesut Ozil and Olivier Giroud.
Arsenal are top of Group F but level on points with Napoli, who overcame Olympique Marseille 3-2 at the San Paolo thanks to Gonzalo Higuain's double.
Added to a cracker from Gokhan Inler, who chested down a clearance on the edge of the area and volleyed home, Higuain's goals meant the pointless French side are out of last-16 contention.
TOTALLY UNMARKED
Chelsea's first goal in a 3-0 home win over Schalke 04 was hardly a classic in contrast, with keeper Timo Hildebrand blasting his clearance against Samuel Eto'o and the ball flying in.
The Cameroonian slotted in a cool second after the break and Demba Ba also scored to put the Group E leaders on the verge of qualification, with the Germans second and Basel third after a late equaliser in a 1-1 home draw with Steaua Bucharest.
Jose Mourinho, who left out Eden Hazard without elaborating why, said he had told Eto'o to close down the keeper.
"I know the keeper from Portugal and Spain because he was there and we know Schalke likes to play back passes and play from the back with the keeper so Samuel was clever in the way he closed him down," the Chelsea coach said.
Barca took the lead on the half hour after Ignazio Abate clumsily pulled back Neymar and Messi did the rest from the spot.
Sergio Busquets then headed in Xavi's free kick and although there was a hint of offside, he was left totally unmarked by a woeful Milan defence which severely pales in comparison to the great back lines marshalled by Paolo Maldini and Franco Baresi.
Milan are 11th in Serie A and the pressure on coach Massimiliano Allegri will now only intensify, although Gerard Pique's own goal from Kaka's cross and a couple of sniffs for substitute Mario Balotelli gave them hope.
World Player of the Year Messi snuffed them out when the Argentine ran through on 83 and finished with a deft chip.
Despite the Nou Camp defeat, Milan remained second in Group H after Ajax Amsterdam beat Celtic 1-0.
Eight police officers needed hospital treatment and more than 15 fans were arrested following violent clashes ahead of the match in the Netherlands.
European champions Bayern Munich and Manchester City, for the first time, qualified for the last 16 on Tuesday.
Image: Lionel Messi of FC Barcelona scores his team's third goal during the UEFA Champions League Group H match against AC Milan at Camp Nou
Photograph: David Ramos/Getty Images