The Empire State Building climbers thought they were on top of the world ... until NYPD officers came climbing right behind them ... armed with body cameras and handcuffs.

Newly released body cam video shows the nerve-racking pursuit from the cops' point of view ... capturing officers scaling the iconic skyscraper's steel spire before finally cornering the daredevil duo -- famed "rooftoppers" Ivan Beerkus and Angela Nikolau -- hundreds of feet above Manhattan.

The footage -- released Wednesday by NYC Police Commissioner Jessica Tisch -- shows officers carefully navigating the narrow metal framework until they reach the climbers. From there, the pair are calmly escorted back down through the maze of beams before they're ultimately slapped in handcuffs.

Tisch praised the officers in an X post alongside the video, writing ... "A glimpse into the work of our Emergency Service Unit. God bless these officers."

As TMZ reported, the climbers sparked a massive response Wednesday afternoon after scaling the 1,454-foot landmark, unfurling a peace banner, and even stopping for a marriage proposal before beginning their descent.

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Even with cops closing in fast, the couple found time to celebrate ... posting their proposal on Instagram, including a close-up of the ring and the moment Ivan got down on one knee.

First comes love, then comes the handcuffs.