This vital victory leaves Blues seventh in the table, but now just two points behind Birmingham in fourth place.
With leading trio Surbiton, Clifton and Canterbury all looking well clear, the race is on the final top four spot.
The Birmingham Uni girls, Leicester, Holcombe and Reading are only separated by two points, but the Sonning Lane club have played a game more than their rivals and currently have a minus goal difference.
Scoring goals has been their main problem this season and so they were relieved to have Richardson-Walsh on duty last Saturday.
The England captain opened the scoring in the 21st minute with a straight flick from a penalty corner, which she repeated on 41 minutes to seal Reading's fifth win in 13 matches.
But the Blues' player-of-the-match vote went to Wiz Hunt, who is working hard to regain full fitness after being injured for most of the first half of the season.
England under-16 player Kym Shergill made a promising league debut, while Alys Richards also did well as she stepped up from the club's 1A team.
"I was very happy with the performance and the result," said coach Merijn van Willigen.
"It was good to see us take a few of our chances, which we haven't always done in previous matches. Kate brings that bit of class when it comes to penalty corners.
"I thought we looked comfortable throughout the game. Birmingham did have a few chances and penalty corners, but we defended well."
Van Willigen added: "This win means we can stay focused on getting fourth spot, but there is a still a long way to go and we are not looking beyond our next game."
Reading meet Bowdon Hightown at Sonning Lane this Saturday (1.30pm).