Despite falling behind to a Jermain Defoe strike, Palace showed they have the fight to beat the drop – even though Paul Robinson should not have been beaten by Johnson's 30-yard strike.
But the draw ended Spurs' recent revival in the top flight under new manager Martin Jol after previously winning five consecutive games in the Premiership.
Crystal Palace had the ball in the back of the net after just eight minutes, but Johnson's close-range effort was ruled out for offside.
Vassilios Lakis shot was only parried by Tottenham keeper Paul Robinson. The ball rebounded Johnson who knocked the ball into an empty net, but was clearly in an offside position.
Fredi Kanoute almost fired the home side into the lead on 27 minutes when he drilled a low shot from the edge of the box, but Gabor Kiraly did well to push the ball around the post.
And the Mali international came close again just two minutes later when he produced a superb turn just outside the area and fired a blistering shot straight into the grasp of Kiraly.
Despite struggling at the wrong end of the Premiership, Palace had two golden opportunities to break the deadlock late in the first half.
On 35 minutes Tom Soares laid the ball into the path of Lakis whose close-range shot deflected inches past the post.
Palace came even closer on 39 minutes when Lakis found Johnson completely unmarked inside the box, but with the goal at his mercy he saw his shot produced a fantastic reflex save from Robinson.
And how they were made to pay as Defoe burst into life early in the second half and got his name on the scoresheet once again.
Defoe's shot on 53 minutes was turned on to the post by Kiraly. But just moments later the England striker made no mistake when he raced unchallenged towards the box.
He planted a sweet shot which bounced off the post and into the back of the net.
But Palace refused to lie down and got their just rewards when they grabbed an equaliser on 79 minutes.
Aki Riihilahti released Johnson into the Tottenham half and the prolific forward fired a 30-yard shot which went through the legs of Anthony Gardner and somehow managed to trickle its way past Robinson into the corner of the net.