Palace have now ended an eight-match winless run, as well as clinching their first home league win of the season, and Townsend says that Saturday's result can act as a launchpad for the rest of the campaign.
Sean Dyche's team, with just a single point from its last six games, finished seventh last season but the Clarets are a team devoid of confidence.
Palace built on its deserved point at Old Trafford last weekend with a win that provides Roy Hodgson's side breathing space - three points - from the bottom three.
Frank de Boer's revolutionary stint at Palace was supposed to see the club turned into a possession powerhouse, dominating games with the ball and playing attractive football.
And Meyer nearly made it two after 35 minutes - his curled left-footed effort beat Hart but went millimetres wide of the post.
The "Eagles" have claimed just two points at home so far this season, scoring just two goals in the process, both of which were penalties.
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And things didn't get better after the break, with Dyche's side indebted to Hart for keeping out Zaha two minutes into the second-half - and the Ivorian fluffed his lines five minutes later, blazing over after being played in by Andros Townsend. His left-footed effort narrowly missed Hart's far post.
Winger Robbie Brady is a month into his comeback from a serious knee injury and is still some way short of the form that played an important role in Burnley's flying start to last season. McArthur could have scored a second, only for Charlie Taylor's sliding tackle to deny him, with Zaha then hitting the crossbar.
Townsend cut in from the right flank on to his left foot and beat Hart with a magnificent shot from outside the box which flew into the top corner. "The effort's good, but it's a but misguided at the moment, we have to remind them how they can play".
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