Both sides had chances in the opening minutes, Barry Robson hitting the bar for the Blades, and Lewis Grabban failing to slot the ball home after a one-on-one with Sheffield keeper George Long.
But after 19 minutes of play it was the Yorkshire-outfit that took the lead, with a close range effort from Murphy, soon after hitting the Bournemouth post.
The second half saw some changes to the Cherries set-up, but they failed to create any clear-cut chances. Dan Seabourne was unable to link up to a Marc Pugh corner, and Grabban failed to make anything of a Brett Pitman through ball.
Later in the match, United had a second goal disallowed after the referee ruled that Dave Kitson had pulled down Matt Ritchie in the penalty area.
The final whistle confirmed Eddie Howe’s first home league defeat since his return to the south-coast club.
The Cherries manager said: “I felt we were the better team and had a lot of possession, but credit to Sheffield United, because they defended well.”
After sitting in top spot earlier this month, Bournemouth have dropped to sixth place in the league, but remain in contention for promotion.
The Blades jumped in front of Swindon to first place with 60 points, but just two points separate them from the Cherries.
United boss Danny Wilson said: “We have fought very hard in the last four matches and we knew a run of wins would get us to where we wanted to be, the job now is to stay there.”
Eddie Howe said: “We now need to win some games, it’s as simple as that. It was a disappointing result, but nothing has been decided.”
AFC Bournemouth: Jalal, Francis, Cook, Seaborne, Painter (McQuoid – HT), Ritchie, Arter, O’Kane, Pugh, Pitman (Fraser – 68), Grabban (Tubbs – 73)
Subs Not Used: Allsop, Hughes, MacDonald, Fogden
Booked: Grabban, Arter
Sheffield United: Long, McMahon, Collins, Maguire, Higginbotham, Flynn, McDonald, Doyle, Robson (Poleon – 84), Murphy, Kitson
Subs Not Used: Westlake, Hill, Ironside, McFadzean, Coyne, De Girolamo
Booked: Robson, Doyle
Main image from AFC Bournemouth Twitter.