Gareth Southgate's side, who lost the Euro 2020 final to Italy on penalties in July, had won their opening five games in Group I.
"An amazing feeling. I'm glad we managed to score that goal in the last minutes. I'm happy," Symanszki said. "I've worked hard for this, struggled with injuries. To play against England, to score a goal, it's a dream come true."
This was England's toughest test in Group I so far with Poland set up to frustrate through defensive play and gamesmanship but the visitors looked set to come through and take a big step towards next year's World Cup finals.
England's efforts were frustrated in the opening 45 minutes as they failed to trouble Wojciech Szczesny in goal for Poland. The hosts' main threat, Robert Lewandowski, meanwhile, was restricted to one half-chance, which was tidily dealt with by Jordan Pickford.
A fast-paced but uneventful first-half burst into life just as the referee whistled for half-time with England and Poland players coming together. Harry Maguire appeared incensed about something, while Poland defender Kamil Glik was called back by the referee as he tried to leave the pitch. Eventually things settled down and both players were cautioned.
There was an incident just before half-time which has been reported to the FA guys," Kane said postmatch. "They're taking care of it and investigating it and we'll go from there. Allegedly it was something that was done, not said. We haven't chance to look at the footage and talk to the lad."
England stepped things up after the break with Jack Grealish and Raheem Sterling troubling the Poland rearguard but, again, without really causing Szczesny too much cause for concern. That was until the 72nd minute when Kane's powerful, swerving shot flew past the former Arsenal goalkeeper from 32 yards out to put England in front.
It was the 15th straight qualifier, for Euros and World Cup, in which Kane has scored and it looked to have brought a sixth straight win in this campaign.
Poland looked short of ideas in response but were almost gifted an equaliser by Pickford, whose clearance was chased down by substitute Karol Swiderski, but the Everton goalkeeper recovered to stop the ball crossing the line.
Then, when England looked to be seeing the game out, a Lewandowski cross was headed home by Szymanski to stun England and grab a point for Poland.
"A kick in the teeth at the end there, it's never easy conceding in the last minute," Kane said. "It was a good performance from the boys though, we controlled the game well. Of course [there was an atmosphere], we're playing for the opportunity to play in the World Cup. Poland clearly saw this as their last opportunity to take some points off us and get closer to us in the group.
"I thought we handled it well. The Hungary game and this game away from home were not easy to play in. The boys stepped up and put in good performances."
England have 16 points from six games with Albania second on 12 points, Poland on 11 and Hungary on 10 points. The top team in the group qualifies for next year's World Cup in Qatar with the second place team heading into the playoffs.