Anthony Gordon put Eddie Howe's side in front at Stamford Bridge with what was his first goal for the club since his January move from Everton, slotting home Elliot Anderson's low cross.
Kieran Trippier's unfortunate own goal levelled matters before the break and that's the way in stayed in the capital, although teenage debutant Lewis Miley went close to netting a memorable winner towards the end when the 17-year-old's effort clipped the crossbar.
After the final whistle, Howe and his players saluted the travelling supporters for one final time this term, with a fourth place finish - and, crucially, Champions League football - secured ahead of the new season.
Club photographer Serena Taylor was there to capture all the best moments for nufc.co.uk.