In the end the Cornish bagged an emphatic 35-22, but the lead changed hands three times and it was neck-and neck until the 72nd minute when the visitors were ahead 22-16.
However, a late surge of powerful attacking play brought three well-executed All Black tries and victory.
Bournemouth showed their intent from the start and were 7-0 up after four minutes. The visiting forwards made good ground and one move ended with flanker Tom Vaughan-Edwards crossing for full-back Dan Pollard to convert.
The Cornish responded immediately with full-back Kieron Lewitt, who had his best kicking boots on, landing a penalty for a high tackle.
Recording his 101st outing for the team, he went on to post a total of 15 points, slotting two more first half penalties and adding the extras to all but the last of his side's four tries.
Within two minutes Bournemouth had stretched their lead to 10-3 with a Pollard penalty for not releasing.
Lewitt's boot narrowed it to one point with his two further goals and the All Blacks took the lead just after the half hour with the visitors under pressure, going offside and deliberately knocking on.
Driving attacking play was then rewarded when Jake Murphy found Liam Yeo and the wing went in under the posts. Back came the Dorset men with a very well-worked threequarter move which brought a try for centre Scott Chislett; so the interval score was 16-15 to the Cornish.
Bournemouth snatched back the advantage when Sam Hardcastle shot away from the base of a ruck to shoot untouched right through the defence to score, with Pollard converting.
Home skipper flanker Tom Rawlings was sin-binned and with him Vaughan-Edwards, who had already had one card for a dangerous tackle, now earning a red card.
But now, six points adrift with seven minutes left, the All Blacks went into overdrive. Centre Lewis Paterson touched down at the posts; number eight Josh Lord went over at the posts after unrelenting pressure close in; and victory was rounded off by Paterson going over for his second.
All Black head coach Cliff Rainford said: "Bournemouth were fighting relegation and that made it difficult for us. We knew we would be in for a hard game and that they would give everything. We had also had a two-week break and had not played at home for five weeks. It was rough and tough but sometimes you have to play ugly to win. At the end we've won and got five points."
