A first-half strike from qualified personal trainer Mark Ricketts, who like Cherries boss Scott Parker came through Charlton's academy, was all that separated the two sides in the incredible tie.
Ricketts, who hadn't played in the last four weeks, took a painkilling injection in order to play what was the biggest game of his career.
But that will be eclipsed in March with Boreham Wood being rewarded with a fifth-round date with Everton.
The full-time whistle sparked jubilant scenes among the 1,400 travelling Wood fans, 500 more than their average National League attendance. Visiting manager Luke Garrard ran onto the pitch to celebrate with his players.
The Cherries, who are third in the Championship, missed a glorious chance to equalise when Philip Billing's lob over goalkeeper Taye Ashby-Hammond.
Ashby-Hammond, who's playing on loan from Fulham, made two brilliant late saves to deny Ryan Christie and Billing.
Boreham Wood are the first non-league side to make the fifth round since Sutton United and Lincoln City in 2017.
The Hertfordshire-based side showed few signs of nerves in the early stages and even gave their hosts a scare as Josh Rees tripped over Nathaniel Phillips' outstretched leg cuing mass appeals from the visitors. Referee Graham Scott was unmoved.
The Wood have the best defensive record in the top five leagues behind Manchester City and they set up to frustrate the Cherries. Unbeaten in 16 games, they were by no means overawed on their trip to the south coast.
Garrard selected three central defenders with wing-backs Jacob Mendy and Kane Smith quickly transitioning to make it a five-man defence when Bournemouth were in possession, which generally they were.
The visitors then sprang a huge shock as they took the lead in the 38th minute. Mendy broke down the left and pulled the ball in to the near post where a careless clearance from Gavin Kilkenny fell to 37-year-old Ricketts on the edge of the area and he scored with a low shot in off the post to send the 1,500 visiting fans wild.
Choruses of 'que sera sera' rang out from the away end as the rest of The Vitality Stadium looked aghast. The grumbles were beginning and it took until the 45th minute for Bournemouth to register their first shot as Lewis Cook fired high over the bar.
The half-time whistle blew and the boos rang out.
Scott Parker responded by making two changes with Todd Cantwell coming on for his debut alongside Ryan Christie with the ineffectual Cook and Ben Pearson making way.
Boreham Wood again had the first chance of the second half as Ricketts' miscued cross almost caught out Bournemouth goalkeeper Freddie Woodman at the far post before the hosts scrambled the ball to safety.
The frustration continued for Bournemouth who were struggling to overcome the sheer desire of their lowly opponents. Parker brought on substitutes three and four of his permitted five with Philip Billing and Jack Stacey tasked with sparking an improvement.
However, the only chance of note until the closing stages came as Christie ran infield to thread a pass through to Billing but his attempted lob fell onto the roof of the net.
Parker's last throw of the dice saw him bring on top goalscorer Dominic Solanke for the final 15 minutes and moments later Bournemouth had the ball in the net.
Christie had again cut inside and shot to the right corner where Boreham Wood goalkeeper Taye Ashby-Hammond tipped the ball up onto the crossbar.
Billing latched onto the rebound and headed against the post before Jaidon Anthony poked the ball over the line before Billing was rightly called offside.
Solanke's moment came during five nail-biting minutes of stoppage time at the end but he pulled his shot inches wide of the far post as the Boreham Wood dugout breathed a sigh of relief before being able to celebrate a famous FA Cup upset.