Sam Kerr was also on target, scoring Chelsea's third goal to wrap up their 3-1 win over Aston Villa.
Steph Catley and Caitlin Foord were on the winning side too, both contributing as Arsenal achieved a league record 13th successive win by beating West Ham 3-1.
But the Matildas' efforts were overshadowed by an extraordinary result at Crawley with Brighton beaten 8-0 by visitors Tottenham, who had been just three points ahead of them in the league.
Raso had only been on the pitch in Manchester for six minutes when she scored, converting the rebound from her own shot after being set up by Jamaica's Bunny Shaw.
Shaw had earlier scored for City only for American Katie Stengel to level.
"We should have put the game to bed a lot quicker than we did, but it was great that Hayley came on and made an impact within six minutes," said City boss Gareth Taylor.
"She contributed again, then it was a case of seeing the game out as there were a few scary moments."
Matildas youngster Mary Fowler was also on the bench for City, coming on for the last 10 minutes.
Lauren James had scored for Chelsea either side of a goal from England teammate Rachel Daly at Kingsmeadow, before setting up Kerr, who held off a defender to score.
Catley, still playing in central defence as Arsenal have an injury crisis in the position, was at fault as West Ham scored a shock opener, her backpass hitting the post before being tucked in by Dagny Brynjarsdottir.
But after Jordan Nobbs levelled it was Catley's superb free-kick that was turned in by Stina Blackstenius to put the Gunners ahead.
Frida Maanum added the third from Katie McCabe's cross after Foord had set the Irish international up to deliver.
The results left Manchester United top from Arsenal and Chelsea on goal difference with Manchester City fourth, six points adrift. Chelsea have played a game more than the other three.
One Australian was on the losing side, Claire Wheeler's Everton going down 3-0 at home to Manchester United.
Australian WSL players Kyah Simon (Tottenham), Alanna Kennedy (Manchester City), Emily Gielnik (Aston Villa) and Mackenzie Arnold (West Ham) were all sidelined with injury, Arnold suffering a calf injury last week that will keep her out for a fortnight.
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