The home side led for much of the game thanks to goals from Adam Le Fondre and a brace from Jem Karacan, but Watford hit back with efforts from Marco Faraoni, Troy Deeney and a last-minute strike from Diego Fabbrini.
The point maintains Watford's unbeaten start to the Sky Bet Championship season and manager Zola was pleased with his team's fighting spirit.
He said: "It feels good not to lose that game. It was difficult to see how we could get anything at half-time when we were 2-0 down.
"I told the players at half-time that it was not enough. I thought we were scratching their back and they were punishing us.
"It pleased me that we never gave up. That is the good thing about this side, sides can score one or two goals against us but we will not be beaten easily. I am delighted we have that quality.
"There are a lot of new players in the squad and lots of them are foreign and maybe they thought that the game builds slowly like in some other leagues, but they need to learn to start games with a high intensity or they will be punished."
Reading took the lead in the eighth minute through a brilliant Le Fondre volley on the edge of the area.
The home side then doubled their advantage before the break when Karacan bundled the ball over the line from close range.
But Watford fought back thanks to a header from Faraoni and a Deeney penalty either side of Karacan's second goal from close range to make it 3-2 heading into the dying moments.
The visitors refused to give in and earned a point right at the end when Fabbrini beat Alex McCarthy to prod the ball over the line from a Lewis McGugan deflected shot.
Reading manager Nigel Adkins was disappointed to see his side fail to hold on for the win but praised the quality of the match.
He said: "It was a cracking game of football. It really was. But for a late deflection we could have won the game.
"We changed our formation to play against a side who are very good. We got on the front foot. It was an excellent goal from Adam Le Fondre and then we did well to go in at half-time 2-0 up and we deserved that.
"They got themselves back in it with a header but then Jem got his second and at 3-1 up you are in a good position and then we gave away a penalty.
"Was it a penalty, wasn't it? It doesn't really matter because it was given by the assistant referee. And then it was game on and very exciting and they got a goal at the end.
"The game was far too open and we gave possession away too easily we could not see the game out thanks to a deflection falling into the path of their player.
"There were a lot of positives going forward and we played good football, and but for a late deflection we could have been celebrating."