Partey was a second-half substitute as he came on for Carrasco on 73 minutes to boost the home side's midfield following sustained attacks from the visiting side.
Luis Suarez scored an 82nd-minute equaliser as La Liga leaders Barcelona maintained their unbeaten start to the season against Atletico Madrid.
Saul Niguez had put the hosts ahead on 21 minutes with a 25-yard curling drive into the bottom corner.
Lionel Messi hit the post with a free-kick early in the second half, before Suarez connected with Sergi Roberto's cross to head in at the far post.
Barcelona are five points clear of Real Madrid, who earlier beat Getafe.
Atletico are third on 16 points, a point behind their city rivals. Read Full Story
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