The midfielder was on target either side of half-time, in reply to goals from Palace's Victor Akinwale and David Obou.
Ben Wilkinson had spoken of the danger Palace would pose our young blues before the match and that threat was evident right from the start.
The home side took the lead just after the ten-minute mark, as striker Akinwale headed home past Josh McNamara from close-range.
We wouldn't be behind for long though as just five minutes later Dickson brought us level following a City counter-attack, firing home his first goal of the season.
However, Wilkinson's side would find ourselves behind at the break, when Obou's curling effort was just beyond the reach of McNamara, seeing the hosts retake the lead.
Following the break, history would repeat itself as Dickson pulled us back level once again just six minutes into the second half.
Neither side could find a winner in the latter stages, seeing the points shared in south London.
HOW WE LINED UP
WHAT IT MEANS
The draw sees us stay top of Group C in the U18 Premier League Cup, with Liverpool and Aston Villa still to play their match.
Finishing in top spot would see us progress through to the quarter-finals automatically.
Our Under-18s will return to league action, as they will take on Liverpool at the City Football Academy in the U18 Premier League.
Kick-off is at midday (UK) on Saturday, 23 October.
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