Jack Patterson booted four majors as the Swans steadied the ship with a 32-point away win over New England in frigid Armidale.
Tamworth rebounded from two straight losses and are in third place on the ladder - assured of a top-four finish - ahead of this week's tantalising final round.
The first-placed Kangaroos and the Swans clash at No 1, while the second-placed Saints and the fourth-placed Nomads meet at Armidale.
Gunnedah are in fifth place and host Moree-Narrabri.
The Swans and the Nomads have the same winning percentage, narrowly behind Inverell.
On Saturday, the Swans led by three points after one quarter, with both sides kicking four majors, and in front they remained - the final score 16.13 (109) to 12.5 (77).
Tamworth led by 30 points at three-quarter time, and the Nomads then kicked the first two goals of the final quarter.
"Excellent, very happy with that," Swans coach Paul Kelly said.
"To have your home game on the opposition's home ground and beat them is pretty good."
Elsewhere, the Kangaroos beat Moree-Narrabri 12.15 (87) to 3.11 (29), while the Saints beat Gunnedah 13.8 (86) to 8.6 (54).
In women's matches, the Bulldogs remained undefeated with a 6.3 (39) to 2.5 (17) win over Inverell. The Swans beat the Nomads 3.10 (28) to 2.7 (19).
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