In many games, this is the goal that buries the conceding team, both due to the margin of the lead that Bournemouth opened up and the manner in which they scored.
Though Giroud took personal pride in his exploits he admitted that the Gunners had made it needlessly hard for themselves with a poor defensive display in the first 58 minutes, when Charlie Daniels, Callum Wilson and Ryan Fraser all took advantage of defensive lapses.
In the 12 minute, Arsenal goalkeeper Petr Cech intervened well in Callum Wilson's run at goal, getting to the ball first.
Bournemouth made it 2-0 when Granit Xhaka gave away the penalty barging into Ryan Fraser just inside the box.
Giroud would inspire a comeback that saw the Gunners earn a point, assisting for Alexis Sanchez and Lucas Perez before heading in the equaliser in the first minute of added time.
Wilson scored the spot-kick, his sixth of the season, despite appearing to stumble and fail to make the connection he wanted on the kick.
Finally Arsenal produced a fluent move, only for Ramsey's effort to be deflected wide.
It was Bournemouth who got the next goal shortly after the break, as Fraser shrugged off the challenge of Hector Bellerin, before slotting through Cech's legs, 3-0.
Bournemouth were worthy of their lead, though, and they nearly added a third in first-half stoppage time when Stanislas wrapped his foot around the ball and curled a 25-yard effort narrowly past the post.
Pep Guardiola's side got back to winning ways by beating Burnley 2-1 at the Etihad Stadium yesterday, a result which took them above Arsene Wenger's men in the table.
Although the midfielder is an important player at Arsenal, considering the Spaniard's age, Wenger is understandably looking at replacing him with no news of a contract extension for him on the horizon. Ramsey started to pull the strings, Alexis Sanchez took the game by the scruff of the neck and Olivier Giroud began to dominate as many expected him to before kick off.
And the Gunners made their numerical advantage tell in the final minutes, as Olivier Giroud directed a header past Artur Boruc.
Perez then netted the goal of the game 15 minutes from time as he fired a perfectly placed left-footed volley into the corner, with Giroud again involved in the buildup.
Dan Gosling could have wrapped things up for Bournemouth with eight minutes left, curling wide of the post after making room for himself inside the area - and within moments the hosts were down to 10 men when captain Simon Francis clattered into Ramsey and was shown a straight red card.