Ricciardo made a brilliant start, his best start of the season, leaping from fifth on the grid to third, behind race leader Lewis Hamilton (Mercedes) and Mexico's Sergio Perez in a Force India.
But it all came to an end on lap 21 of the 43-lap race on the very fast Spa-Francorchamps circuit with the Red Bull stopping trackside with power failure after an entertaining tussle with Perez.
The race was a nailbiter towards the end.
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READ NOWHamilton led from teammate Nico Rosberg, with Ferrari's Sebastien Vettel third.
But Vettel gambled on just one tyre stop and with a few laps remaining, Frenchman Romain Grosjean in the Lotus was fast closing in.
On the last lap, the Ferrari's right rear tyre disintegrated at about 300km/h and an emotional Grosjean shot past for his first podium spot since 2013.
Fourth was Ricciardo's teammate Daniil Kvyat, followed by Perez and Felipe Massa's Williams.
Ferrari's Kimi Raikkonen, who started from 14th, put in a brilliant drive to finish seventh, with young Dutchman Max Verstappen finishing eighth in a Toro Rosso.