Burcher led teammate Jordyn Sinni, clocking a 1:31.6540s in the dying moments of the 20-minute session.
Eggleston locked out the front row ahead of Triple Eight pair Ben Gomersall and Jackson Walls.
Rylan Gray was the leading Tickford Autosport driver in fifth while Brad Vaughan made a marked day-on-day improvement for Brad Jones Racing to qualify sixth.
Last year’s champion Zach Bates was seventh ahead of Elliott Cleary and Lochie Dalton.
Cameron McLeod, who took pole position and the race win on Saturday, was only 10th for Kelly Racing with a time half a second away from the fastest Burcher lap.
Race 1 runner-up Jobe Stewart struggled in the second qualifying session. The Image Racing driver was only 19th in the 23-car field.
Ayton Hodson was another struggler. Having qualified on the front row for Race 1 and finished that affair in fifth, he wound up only 20th for Anderson Motorsport.
Race 2 of the Dunlop Super2 Series is scheduled for 2:40pm AEDT.
Results: Dunlop Super2 Series Sydney 500, Qualifying Race 2
| Pos | Num | Drive | Time | Diff | Gap |
| 1 | 36 | Cody Burcher | 1:31.6540 | ||
| 2 | 54 | Jordyn Sinni | 1:31.7459 | 0.0919 | 0.0919 |
| 3 | 35 | Ben Gomersall | 1:31.8198 | 0.1658 | 0.0739 |
| 4 | 11 | Jackson Walls | 1:31.8348 | 0.1808 | 0.0150 |
| 5 | 55 | Rylan Gray | 1:32.0088 | 0.3548 | 0.1740 |
| 6 | 80 | Brad Vaughan | 1:32.0110 | 0.3570 | 0.0022 |
| 7 | 1 | Zach Bates | 1:32.0495 | 0.3955 | 0.0385 |
| 8 | 38 | Elliott Cleary | 1:32.1425 | 0.4885 | 0.0930 |
| 9 | 6 | Lochie Dalton | 1:32.1716 | 0.5176 | 0.0291 |
| 10 | 92 | Cameron McLeod | 1:32.1740 | 0.5200 | 0.0024 |
| 11 | 9 | Cody Gillis | 1:32.1924 | 0.5384 | 0.0184 |
| 12 | 5 | Reuben Goodall | 1:32.2051 | 0.5511 | 0.0127 |
| 13 | 118 | Jarrod Hughes | 1:32.2632 | 0.6092 | 0.0581 |
| 14 | 33 | Bailey Sweeny | 1:32.3038 | 0.6498 | 0.0406 |
| 15 | 222 | Nash Morris | 1:32.3110 | 0.6570 | 0.0072 |
| 16 | 2 | Campbell Logan | 1:32.3452 | 0.6912 | 0.0342 |
| 17 | 17 | Ryan Tomsett | 1:32.3518 | 0.6978 | 0.0066 |
| 18 | 22 | Mason Kelly | 1:32.4285 | 0.7745 | 0.0767 |
| 19 | 99 | Jobe Stewart | 1:32.4351 | 0.7811 | 0.0066 |
| 20 | 28 | Ayrton Hodson | 1:32.4977 | 0.8437 | 0.0626 |
| 21 | 88 | Bradi Owen | 1:32.5129 | 0.8589 | 0.0152 |
| 22 | 53 | Max Geoghegan | 1:32.8766 | 1.2226 | 0.3637 |
| 23 | 25 | Matt Hillyer | 1:33.1831 | 1.5291 | 0.3065 |
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