Charlie Daniels struck in the 90th minute after goals either side of the break for Bournemouth, including an own goal from Newcastle defender Steven Taylor in the 28th.An Ayoze Perez goal 10 minutes from time gave Newcastle false hope.
Newcastle's third straight defeat leaves them in 19th place on 24 points with just nine games left.
Bournemouth has 35 points and is moving closer to Premier League survival.
McClaren, who appears to be fighting for his job, said: "There are 10 games to go and we have to show fight." He urged his players "to stick together."
With so many fans demanding McClaren's dismissal, owner Mike Ashley is left with a tough decision over the future of his manager, who only joined the club last summer.
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