The Attorney gave the team their first win of the evening when taking the seven-furlong race under Adam Kirby, with trainer Charlie Hills then gaining a second victory later on the card when Menai Bridge was a winner under Saffie Osborne.
The team have now tallied 188 points and are therefore 10 points clear of second-placed Team ThoroughBid.
Osborne leads the individual rider rankings as a result of her performance and has racked up 132 points in total so far, one in front of Jack Mitchell.
"We are smashing it tonight," Team Swish racing manager Rosie Tapner told Sky Sports Racing.
"I'm going to go over the top here because it's so exciting, two winners and we are flying above the leaderboard, it's great!
"I have ridden both horses, I can't take credit for them but I'm going to tonight!
"They're such lovely horses, I am so thrilled and Saffie must be as well.
"She has done amazingly, she's just absolutely flown and we've loved having her.
"We can give it over to Kieran Shoemark and Adam Kirby as well, we've got a great team.
"I'm hoping we can keep on flying up and if we dip down, we'll give others a chance and then throw it back at Newcastle."
Team ThoroughBid had Hayley Turner gaining a second series victory, this time courtesy of Richard Hannon's Typhoon Ten who was triumphant by a short head in the six-furlong race.
Team talkSPORT enjoyed a winner with Roger Varian's Lydford, who was steered to victory by Mitchell as the well-backed 6-4 favourite and lifted his team into fifth place.
Goat Racing also had a triumph on the evening and are now third thanks to Louis Stewards' performance aboard Charlie Fellowes' Billhilly.
Marco Ghiani was the victim of a heavy fall in the second race when his saddle slipped and he was unshipped from Stuart Williams' Papa Stour in the closing stages of the contest.
Thankfully the rider was not seriously harmed and was seen getting to the feet on the track, but did not take up his one remaining ride on the card.