The Cherries had to ride their luck for large parts of the second half, but the home side's failure to convert their chances proved costly in the end.
Here, Sports Mole takes an in-depth look at how the 90 minutes of action unfolded in West London.
On target: 6
On target: 5
Was the result fair?
On the basis of the full 90 minutes, Bournemouth will argue that they executed the perfect gameplan at Stamford Bridge. While the first half was evenly matched in the grand scheme of things, with the Cherries possibly just edging things in terms of chances created, the second half was more about remaining defensively resilient and providing a late sucker-punch to claim the points.
Make no mistake about it - one point would have been celebrated like a victory among those travelling supporters. That was made clear when, with nine minutes on the clock, a rare attacking move ended with the ball rolling out for a corner kick. Loud cheers went up from that one section of the ground, but there was far better to come as Murray - on the field for 99 seconds - turned the ball home following some slack Chelsea defending.
Jose Mourinho can point to the 19 shots his side fired in, yet less than a third of those were on target and Artur Boruc was never truly troubled. They may have ridden their luck throughout the second period, but take nothing away from this historic Cherries win. Not since Charlton Athletic did likewise in 2001 has a side promoted from the second tier won at Stamford Bridge, while it is only the second time that Mourinho has lost to a promoted side in 31 encounters. A new record is seemingly being created by Chelsea as each week passes by, though unfortunately for them it is often for all the wrong reasons in this season to forget.
All the talk pre-match heading into this evening's contest surrounded the Blues' hopes of finally making up some ground on those above them. Results very much went Chelsea's way on the whole in the earlier kickoffs, meaning that the gap on the top four - their realistic target at this stage - could be reduced to 11 points. As it is, following yet another defeat, they now find themselves two points above the drop zone.
Those home supporters leaving Stamford Bridge may start to truly feel that the deficit on the Champions League spots is now simply too much to make up, particularly on the back of a fourth home defeat this term already. The home of the champions was once the biggest fortress in English football; now it is a hunting ground for teams at the bottom end of the table who can sense a major upset. Just ask Crystal Palace and Southampton, both of whom were struggling a little at the time before winning here, and also Liverpool who put four past the Blues recently.
After a run of three games without defeat, including a performance Mourinho described as his side's best of the season last time out at Tottenham Hotspur, this was meant to be the evening that momentum continued to build. That certainly looked to be the case when Eden Hazard, fielded up top in absence of Diego Costa once more, got in a promising position a little over a minute in. Real chances proved to be few and far between, though, and in the end the attacking - and indeed the defensive - frailties came back to haunt the hosts.
Just when things were beginning to look a little daunting for Eddie Howe and his side, with a place in the bottom three and games against Chelsea, Manchester United and Arsenal to come before the year is out, the Cherries produced this performance which will renew spirits in the campaign. The 3-3 draw against Everton last week was special, of course, yet nothing will quite top this result in their maiden top-flight campaign.
It was a performance built on bravery more than anything in the opening 45 minutes, as Junior Stanislas and Josh King both came close to beating Thibaut Courtois on his grand return to the Chelsea's starting lineup. For so long in the second period it looked as though their efforts would ultimately count for nothing, with Howe rather reluctant to change things around despite his side seemingly tiring by the minute.
When the young boss did finally roll the dice, the move more than paid off as Murray was there to pounce at the end. Not only did the South Coast side become the first team in 389 minutes to breach Chelsea's backline, but they also stood strong to claim just a second clean sheet of the campaign. It may have been a different story entirely had their opponents tucked away one of their many half-chances, but those travelling fans will not care whatsoever following this dream result.
Sports Mole's man of the match
Simon Francis: Produced a superb defensive display at the back to keep the hosts' chances down to a bare minimum. Pulled off six successful clearances, two tackles in wide areas, won three aerial duals, two interceptions and also completed a couple of take-ons just for good measure.
Perhaps Chelsea's defence can be forgiven for switching off a little late on after dominating large parts of the second half. This is the Premier League, however, and each of those players knows that you cannot switch off for a second in this division. A corner into the box was flapped at by Courtois, before the ball was allowed to come back across goal where Murray was left in space to divert home.
A couple of big calls for Mike Jones to make, the first of which arrived on the hour mark. Costa's low cross into the box struck the arm of Francis on its way through, yet the defender knew little about it and there was very little distance between himself and the ball when it was initially stuck. Mourinho also felt that Murray was in an offside position for the winner, but in a crowded box it was extremely tough to make out.
Chelsea: The Blues will be desperate to get their campaign back on track once and for all when they take on Premier League surprise package Leicester City, but first is a European tie against Porto in midweek.
Bournemouth: This momentous occasion provides the Cherries with fine preparation for their next outing, which comes at home against Manchester United in seven days' time.