Tomic dropped the first set to the big-serving German as Brands edged a tense tie break by seven points to four.
The second set looked to be heading for a similar conclusion but late on Tomic earned a crucial break to draw level.
Brands continued to use a potent serve to trouble Tomic but started to wilt in testing conditions as the temperature hit 40 degrees in Melbourne.
Once again both men could not be separated before a tie-break in the third set, which Tomic edged in a topsy-turvy finish.
The crowd favourite squandered seven match points in the fourth but finally got over the line in another tie-break tussle which saw both players miss big chances across 18 points.