The Seahawks made it five wins out of six games to surge into sixth spot and close the gap on fifth-placed Ivanhoes to just one point.
Septimus Ambrym grabbed two tries, while Ross Maloney, Merton Richards, Cyprian Mossman, Edward Dabah and Bert Harris also crossed for the hosts.
Yarrabah coach Vincent Schreiber said his in-form side dedicated their victory to club stalwart Shavanne Fourmile, who sadly passed away recently.
It was a big motivation for the boys to win for Shavanne, and they continually play not just for themselves, but our whole region, said Schreiber.
Tully came up here with an intensity to try and beat us through their big forwards, but they soon realised that we were ready to play footy.
Our discipline has been really good over the past six weeks, and our attitude has also been spot on.
Weve been talking about making the finals since day one, and at the moment the boys are feeling on a high and were steering ourselves towards our goal.
To try and make the finals, Yarrabah will most likely need to win their last three games, which include two home matches against finals rivals Mareeba and leaders Kangaroos.
Second-placed Suburbs got their 2013 season back on track with a hard-fought 22-18 victory over finals-chasing Innisfail at Callendar Park.
Both sides scored four tries, but the boot of Josh Babsek (three conversions) led the visitors to a vital two points.
It was only Suburbs second win in five games, after recent narrow losses to Yarrabah, Mareeba and Ivanhoes.
Mareeba and Ivanhoes were also involved in a thrilling encounter at Davies Park on Saturday night, with the third-placed Gladiators clinching a 32-26 win over the fifth-placed Knights.
Mareeba player-coach Rod Jensen (two tries) again got himself on the scoresheet, while Jason Lea crucially slotted over six goals with both teams crossing for five tries apiece.
Reigning premiers Brothers again showed they are running into form at the right time, handing bottom-of-the-table Atherton a heavy 56-0 home defeat.
Full-back Ben Fitzpatrick and winger Sam Bann both celebrated hat-tricks in the 11-try romp, which sees the Brethren remain in fourth spot on the ladder.
Meanwhile, Edmonton Storm recorded their biggest victory of a disappointing season when they thrashed Mossman-Port Douglas 60-0 at Barlow Park.
Harry Cobb, Clifton Tildora and Brett Campbell all grabbed doubles and Brian Murgha landed seven goals as the hosts racked up 10 tries to nil.
Top-of-the-table Kangaroos had a bye.
2013 Bendigo Bank A Grade ROUND 18
Saturday 20 July
Brothers 56 (Fitzpatrick 3, Bann 3, Doolah, Naawi, McIntosh, OFarrell, Groves tries; Sibley 6 goals) def Atherton 0 at Atherton Showground.
Suburbs 22 (Sutherland, Prior, Singleton, Henley tries; Babsek 3 goals) def Innisfail 18 (Sofa, Pratten, Watson, Mani tries; Biondi-Odo goal) at Callendar Park.
Mareeba 32 (Jensen 2, Aue, Roos, Sio tries; Lea 6 goals) def Ivanhoes 26 (Barnard 2, Lynch, Romano, Kyle tries; Furphy 3 goals) at Davies Park.
Sunday 21 July
Yarrabah 36 (S. Ambrym, Maloney, Richards, C. Mossman, Dabah, Harris tries; C. Murgha 2, Mundraby, Harris goals) def Tully 18 (Tauli 2, Dimauro tries; Ketchell 3 goals) at Jilara Oval.
Edmonton 60 (Cobb 2, Tildora 2, Campbell 2, Doolan, Tatipata, Ford, Quakawoot tries; B. Murgha 7, Saumalu 3 goals) def Mossman 0 at Barlow Park.