Philip Billing had given the visitors a shock early lead, turning in the second-fastest goal in the history of the Premier League as he broke the deadlock with just 9.11 seconds on the clock.
Marcos Senesi doubled the lead with a header three minutes before the hour-mark before the Arsenal fightback began when Thomas Partey tapped home.
White then scored his first-ever Arsenal goal to level the game before Nelson provided the moment to remember in the dying embers.
It is the third time in their last six games that Mikel Arteta’s side have scored a winner in or after the 90th minute and, for White, that is no coincidence.
“That is football, the emotions of the game and the different ways it could have gone,” he told Arsenal Media.
“I think it is all down to the boys and how we work each day, it is a result we fully deserve.
“Every week we keep building and winning games and that’s what we managed to do today…We just keep going, play the way we play and the goals will come.
“It (scoring the equaliser) was unbelievable. It was Reiss that crossed it for me, so I’m very grateful.”
— Arsenal (@Arsenal) March 5, 2023
Nelson was introduced for his first appearance since mid-November having also worked his way back to fitness from a thigh injury.
The 23-year-old now has the most goal contributions of a substitute in the league this season, despite just three appearances across the campaign so far.
“I didn’t start the game, but I came on with the instructions just to play forward, try and get as many one-on-one opportunities as I can to create something, and I did,” Nelson said.
“It’s just amazing to celebrate with the supporters and the support we get, so hopefully we can carry it on for the next few games.”
For a large period of the game, Bournemouth appeared on course to take themselves out of the relegation zone, only to be left bottom of the pile following Nelson’s late heroics and Southampton’s win over Leicester.
“My initial thought and feeling is that I’m obviously devastated at the last goal,” manager Gary O’Neil said.
“It has come so late and one he won’t hit like that too often, it was a big blow. It is a tough place to come, they have fantastic players and are very well coached.
“We came up a fraction short from taking a point away from the league-leaders, there is definitely something in that. From where we have been in the past few years and where we are trying to get to it is a big effort to push them as close as we did.”
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