The Indian ace had five birdies against one bogey and moved to Tied-17th with a six-under 138 after 36 holes at the Lake Karrinyup Country Club.
Two other Indians, SSP Chawrasia (71-68) and Chiragh Kumar (70-69) were Tied-26th, while Gaganjeet Bhullar (72-69) was T-41st.
They all crossed the first hurdle of the cut after 36 holes, which fell at one-under 143 at the A$1.75 million event tri-sanctioned by the Asian Tour, the ISPS HANDA PGA Tour of Australasia and European Tour.
There will be a second cut after 54 holes and only the Top 24 will proceed to Matchplay on Sunday. Each match will be a six-hole affair. The top-eight players after the third round will be rewarded with an automatic seeding into the second matchplay round.
Four other Indians, Shiv Kapur (70-73) and Jyoti Randhawa (71-72) at T-68, S Chikkarangappa (71-73) at T-88th and Rahil Gangjee (75-81) at T-154th missed the first cut.
"It felt good to hit it nicely off the tee and hole some putts. With Amritinder, my coach, around I have been working on some small adjustments in my swing and it helped here. This is a great format and makes it interesting. I am going to give it all to make it to the knock-out on Sunday,"Jeev said.
Rumford progressed into the third round with his two-day total of 13-under-par 131 and remains well poised to make it into Sunday's round.
Australia's David Bransdon, who had earlier taken the morning clubhouse lead, was also well positioned to take his place among the top-24 as he posted the day's lowest score of 64 to take second place.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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