It was almost all three for the in-trouble Cherries though as Callum Wilson's late overhead kick found its way into the net.
However, VAR correctly chalked it off as the ball hit the hand of Wilson's teammate Josh King en route to goal.
They really should have scored in stoppage-time when Harry Wilson was put clean through on goal but Hugo Lloris was equal to his effort.
But Spurs will feel aggrieved that they didn't get a penalty inside the first five minutes, however.
Harry Kane was felled in the box after being clumsily pushed in the back by King but VAR decided not to award a spot-kick.
Neither side created too many clear-cut chances in a match that also saw Adam Smith receive oxygen and get stretchered off following a clash of heads with Ben Davies, leading to twelve minutes of stoppages being added on at the end.
The result means Eddie Howe's side are still in the relegation zone but are three points off rivals Watford and West Ham.
Meanwhile, Spurs' hopes of finishing in the top four are all-but over as they are now ten points behind fourth-placed Leicester with four matches left.
In the other 6pm kick-off, Danny Ings carried on his impressive form in front of goal as Southampton claimed a 1-1 draw at Everton.
Ings gave Saints the lead with a poacher's finish just after the half hour mark - the goal putting him level with Mohamed Salah in this season's goalscoring charts. Pierre-Emerick Aubameyang and Jamie Vardy are still ahead of Ings with 20 and 22 strikes respectively.
However, the spoils were shared with Richarlison grabbing Everton's equaliser just before half time.
The late kick-off saw Manchester United visit Aston Villa, and Mason Greenwood lit things up yet again as he helped fire the Red Devils to a comfortable 3-0 win.
The 18-year-old's brilliant strike on the stroke of half time put the Red Devils two up after Bruno Fernandes' penalty had given them the lead.
There were critics of the decision to award Man United the spot-kick, given Fernandes appeared to step on Ezri Konsa rather than the Portuguese being fouled.
Nonetheless, Ole Gunnar Solskjaer's men were superior to their relegation-threatened opponents and they got a deserved third thanks to a composed strike by Paul Pogba.
The result puts United on the cusp of the coveted top four as they're just a point behind fourth-placed Leicester.
Meanwhile, Villa are getting ever closer to losing their top flight status as they're now four points off safety with four matches to go.
Bournemouth's Premier League survival bid has been given a boost as they played out a goalless draw at home to a passive Tottenham side.