The Spaniard scored a stoppage-time equaliser to salvage a 2-2 draw in an end-to-end game at the Emirates.
The referee pointed to the spot after the Belgian went to ground following a swing of the boot from Bellerin, who ended up being the hero when he netted in the 92nd minute following what Marcos Alonso had hoped was the winner for the Blues.
After the final whistle blew, Bellerin told Sky Sports News: "It was non-stop football, running up and down. We worked hard all week. It was a great reaction towards the end.
"[Hazard is] very quick in the box - I saw the ball in the air and tried to challenge for it. We both got to the ball at the same time and the referee thought it was a penalty.
"It was great to score. I haven't scored in a while. I'm happy with the goal and the reaction of the whole team."
Arsenal remain sixth in the Premier League table, five points adrift of the top four.