Their version of Smith's hit - recorded as this year's official Comic Relief song - held off Years & Years' track King by 9,000 combined chart sales.
Smith's original album rendition was at number 19 after 45 weeks on the chart.
But the singer was knocked off the top of the album chart by rapper Kendrick Lamar, who scored his first UK number one with To Pimp a Butterfly.
Last week it was revealed the album had set a new record on Spotify after it had been streamed 9.6 million times worldwide in one day.
Elsewhere in the singles chart, FourFiveSeconds by Rihanna, Kanye West and Paul McCartney climbed two places to number three.
The Official Charts Company said the song was the week's most-streamed track with 1.98 million streams.
James Bay's Hold Back The River climbed six places to four, while Ellie Goulding completed the top five with her former number one, Love Me Like You Do.
In the album chart, Dire Straits' Mark Knopfler entered the chart at three - the highest-charting album of his career - with Tracker.
Ed Sheeran's X was at number four after 39 weeks in the chart, with Van Morrison's latest record, Duets - Re-working The Catalogue, another new entry at five.
REM's 1992 album Automatic For The People also made its first top 40 appearance in 15 years, re-entering at number 40.
Sam Smith and John Legend have topped the UK singles chart for a second week with their duet Lay Me Down.