Abraham has spoken in the past about how former Blues striker Drogba was an inspiration to him during his formative years at Chelsea.
And Drogba - who is still playing for USL side Phoenix Rising in the United States - took to social media after the on-loan Chelsea youngster opened his account at the same Selhurst Park ground as the Ivorian did in English football in August 2004.
"Great to see you opening ur account in a stadium where I scored my first @ChelseaFC @premierleague goal @tammyabraham," Drogba tweeted.
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Abraham showed strength and composure in front of goal to fire Swansea ahead a minute before half-time and enliven what had been a drab contest.
The 19-year-old shrugged aside Palace substitute Martin Kelly at the far post to volley home Leroy Fer's cross from close-range.
It was Swansea's first on-target attempt in the Premier League this season and Abraham's second goal in as many games following his midweek strike in the 4-1 Carabao Cup victory at MK Dons.
"At this level there's a lot of scrutiny when a striker doesn't score for two games," Swansea head coach Clement said after Abraham had been shut-out by Southampton and Manchester United in the opening two league games.
"But he's new to the level and the fact he's now off the mark in the Premier League is good for him.
"He scored in midweek as well, he is a goalscorer and he's very happy he made that contribution.
"A lot of questions were already being asked that we're not creating goals or scoring goals.
"That was after two games, but the next two games we've scored sixand the strikers are scoring.
"Jordan (Ayew) and Tammy have backed up their midweek goals in the Premier League. That's a positive."
Palace boss Frank de Boer had described the game as "must-win" after opening losses to Huddersfield and Liverpool.
But the Eagles are still looking for their first goal and point of the season after a defeat which leaves them one place off the bottom of the Premier League.
"We try to get points in every game and it is very disappointing for everybody who loves Crystal Palace," De Boer said of Palace's poor start to the campaign.
"We want to get off the mark with some goals and points, but we did not achieve it.
"It looks like (lack of) confidence because there were so many moments to hurt Swansea in the first half.
"There were a lot of moments where we could play on the ground, but we were not comfortable on the ball."
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