Scotland international Caroline Weir volleyed the visitors into the lead but England star Alessio Russo scored twice to give the Gunners a second win from their four WCL matches.
Defender Catley played the full match and had the misfortune to send her headed clearance of a curling free-kick into the path of Weir who blasted the opener just before halftime.
Foord came on as one of five substitutes and midfielder Cooney-Cross had some nice touches before being replaced in the closing minutes.
Russo's looping header from a right-wing cross early into the second half drew Arsenal level and she scored with another header, this time from Beth Mead's left-wing corner, in the 67th.
The victory came as welcome relief for coach Renee Slegers' Arsenal who were without a win in their last three matches across all competitions, one of which came in Europe, where they were stunned by Bayern Munich last week.
"Proud, I think not ideal going 1-0 down from a set piece at the end of the first half but we all stayed very calm. Coaches, tech staff and players in the changing room spoke about a couple of details," said Slegers.
"Really happy with how the players stayed so calm on the pitch in the second half because it's not an easy scenario where there was already pressure on us ahead of this game."
Manchester United fell to their first defeat in the league phase after being beaten 5-2 by Wolfsburg.
United's Fridolina Rolfo struck against her old club, but two goals from Ella Peddemors put Wolfsburg ahead and a chaotic end to the first half saw Lineth Beerensteyn score before Melvine Malard immediately responded.
Beerensteyn added a fourth after the break and Vivien Endemann struck at the death to end United's three-game winning run.
Eight-time champions Lyon came from 3-0 down at half-time to snatch a 3-3 draw at Juventus.
Goals from Chiara Beccari, Michela Cambiaghi and Tatiana Pinto put Juve in control at the break.
But Tabitha Chawinga pulled one back and Marie-Antoinette Katoto's header made it 3-2.
Lyon were awarded a penalty in the 89th minute after Cecilia Salvai handled and Wendie Renard tucked home the spot-kick.
Goals from Maeline Mendy and Maelle Garbino gave Paris FC a 2-0 win over Benfica, who had Caroline Moller sent off in the first half, while Valarenga drew 2-2 at home to St Polten.
