Relegation-threatened Bournemouth scored the second-quickest Premier League goal of all time after nine seconds of play through Philip Billing, and despite Arsenal’s domination, Marcos Senesi made it 2-0 for the visitors before the hour.
But then began an Arsenal comeback that could prove a pivotal moment in the title race.
Thomas Partey prodded a shot past Bournemouth keeper Neto just past the hour mark, and eight minutes later substitute Ben White’s volley crossed the line despite Neto’s desperate dive.
With the Emirates Stadium crowd roaring their side on it appeared Bournemouth had held on for a precious point in their fight against relegation, but substitute Nelson’s sensational strike seven minutes into stoppage time sealed a remarkable win.
Arsenal restored their five-point lead over Manchester City, who had won earlier, with 63 points from 26 games.