A Jason Green century led the Blues to 7-273 on day one of the clash last week and then the Macquarie bowlers did the job, dismissing Newtown 90 runs short of the target.
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The win was set up early on day two as Jeremy Dickson (4-46) helped leave the Tigers reeling at 5-69 after 20 overs.
"It's all on us now," Blues captain Keiran Brien said after the win.
"The boys will be trying for one another to be there and if not then we've only got ourselves to blame.
"It's good coming into the final rounds with two tough games so it will really get us ready for semis if we're good enough to make it."
Next round is another big one for Macquarie, taking on defending premiers RSL-Colts.
They head into the showdown with plenty of confidence after Saturday's impressive effort with the ball.
Dickson starred, removing Wayne Dunlop (0), Mat Skinner (2) and Tom Barber (1) early on.
Fellow new ball bowler Ben Taylor was also at his best again and finished with 3-35, leading Brien to again praise his bowling attack.
"'B.T' (Taylor) has been a big boost for us this season but even last season we worked on bowling tighter," Brien said.
"We had some younger guys who would try and get a wicket every over rather than tight two-day bowling and building pressure but 'B.T' has brought that experience across and he's even helped 'Dicko'.
"They help us set the platform so it's very handy."
The only negative, according to Brien, was the fact more than 100 runs were scored by Newtown's final four batsmen.
Steve Skinner (46) had earlier been the only batsman to spend some meaningful time in the middle but Tom Skinner (47) and Mitch Gray (42) frustrated the Blues as the Tigers went on to finish with 183.
"It (the win) shows we're coming good at the right time but I would have liked it to have been a bit more," Brien said.
"We'd done all the hard work in the first 20 overs and got most of the wickets and then it dragged on a bit so it was a bit frustrating."
The captain added next round's match with Colts will show him where his side is at as the business end of the season arrives.