Heath drilled home in the second of six added minutes to ensure the visitors avoided a second straight defeat in the league following their shock loss to Birmingham a fortnight ago.
Khadija Shaw had given City the lead in controversial circumstances after 65 minutes, the Jamaican international tapping home from close range from Lauren Hemp’s low cross.
Arsenal were furious that play had been allowed to continue when the ball deflected off the referee in the build-up to the goal, but their protests fell on deaf ears and head coach Jonas Eidevall was booked for his complaints.
The result leaves Arsenal two points clear of Manchester United who had earlier kept up the pressure with an impressive 3-0 win against Tottenham.
Vilde Boe Risa volleyed the hosts into the lead after 38 minutes before Hayley Ladd netted a second ahead of the interval and Leah Galton sealed the win in the second half as United recorded their sixth victory in as many matches.
United were able to take advantage of Chelsea’s goalless draw at Brighton.
Erin Cuthbert came the closest to scoring for the Blues when her second-half strike cannoned off the crossbar.
Chelsea had 26 attempts but were unable to find a breakthrough – the first time Emma Hayes’ side have failed to find the back of the next in 60 WSL matches, a streak which stretches back to October 2018.
Aston Villa ended a four-match losing run with a 2-1 win at Leicester.
Jemma Purfield’s own goal provided the visitors with the lead after just four minutes before Leicester were back on level terms with 14 minutes remaining when Villa goalkeeper Hannah Hampton turned Purfield’s corner into her own net.
But Alisha Lehmann struck deep into stoppage time as Villa took all three points.
Reading secured a brilliant 3-2 comeback win against bottom side Birmingham to record a fourth straight WSL victory.
Gemma Lawley and Jade Pennock fired the Blues into a 2-0 lead inside 36 minutes.
But Justine Vanhaevermaet pulled one back in first-half stoppage time before Natasha Dowie scored Reading’s second from the penalty spot moments after the interval.
Emma Harries then completed the fightback with an impressive volley after 55 minutes.
West Ham secured a comfortable 3-0 home win against Everton to move up to seventh in the table.
Katerina Svitkova opened the scoring for the Hammers with four minutes of the opening period remaining before Dagny Brynjarsdottir doubled her side’s tally shortly before the hour mark.
Claudia Walker made sure of the victory when she netted a third in the closing stages.