Milner-Olsen was solid but something had to change following their dismal second period and the combative Daya Wiffen was added to the centre position as Lees moved to wing attack.
The Pulse worked their way in to the contest led by skipper Katrina Grant who claimed a game-high seven intercepts.
But they left their run a bit late, and although they got within one goal in the fourth quarter they failed to convert their opportunities as they coughed up the ball or couldn't get their shots to drop.
Swifts goal shoot Susan Pratley said after the game that her side had a lot to work on.
"We did get out of jail. A win's a win but we shouldn't have let them back in the game and we just did some silly, silly things and it's something we need to address.
"The Pulse came out and really stepped up the intensity and we just didn't go with it. So I'm not sure really what we have to look at but we'll have to go over the video and have a look ... I'm sure there's plenty to work on after that."
Broughton will have plenty to look at too in terms of who will sport the WA bib next. Although it appears Lees is the most competent option she is the team's best centre.
Wiffen has shown patches of form at centre and played well there when the Pulse beat the Tactix in round four and could be used there more often.
Another concern for Broughton will be the goal attack position after Paula Griffin struggled today, turning over the ball four times in just over a quarter before she was substituted for Jamilah Gupwell.
It remained unclear whether the change was tactical or injury-enforced but Gupwell shot only two from six and had little impact on the game as Amber Bellringer sat on the bench unused.
Next week the Pulse host the Magic in Porirua and the Swifts meet the Melbourne Vixens in Sydney.
NSW Swifts 39 (Susan Pratley 20/23, Amorette Wild 11/14, Carla Dziwoki 3/5, Kimberly Borger 5/6) Central Pulse 36 (Caitlin Thwaites 30/38, Jamilah Gupwell 2/6, Paula Griffin 4/5) 1Q: 13-9, HT: 24-15, 3Q: 32-27
