Walker scored a brilliant solo try and landed four goals and a field goal while Suaalii grabbed a double as Trent Robinson's men chalked up their sixth win of the season.
The Roosters made the perfect start when veteran big man Jared Waerea-Hargreaves threw a dummy and bamboozled Reagan Campbell-Gillard before carrying Reed Mahoney over the line to score in the fourth minute.
Eels halfback Mitchell Moses put his stamp on the game in the 10th minute when he produced a superb show-and-go on halfway to split the Roosters open before finding Isaiah Papali'i backing up on the inside to score.
Three minutes later it was Roosters skipper James Tedesco bagging a try after chasing through a Walker grubber which was fumbled by Clint Gutherson.
Tedesco was in the thick of the action again in the 16th minute when he was tackled without the ball by Tom Opacic close to the tryline and the Eels centre was sent to the bin. Walker landed the penalty goal to make it 14-6.
Having laid on a try for his skipper with the boot Walker then did it all on his own with a brilliant chip and chase try in the 25th minute and Trent Robinson's men were out to a 14-point lead.
Bailey Simonsson looked set to pull one back for the Eels but he was pulled up for a double movement after a great cover tackle by Angus Crichton cut him down just short.
With 10 seconds remaining in the first half Walker calmly potted a field goal to make it 21-6 at the break.
Suaalii crossed early in the second half after good lead-up work by Luke Keary and Joseph Manu before the Eels hit back through a rampaging Papali'i.
Two minutes later the Eels were right back in the contest thanks to a superb individual try by Moses which saw him scoot down the touchline and kick back inside for himself before getting a second kick on the ball and touching down to pull Parra within seven.
Ryan Matterson made it three tries in 10 minutes when he stormed over and the Roosters' lead had been cut to one point.
Suaalii made it a double in the 62nd minute when he soared through the night sky to pull down a Keary bomb and the Roosters had steadied the ship at 29-24.
A high tackle by Dylan Brown on Sitili Tupouniua with seven minutes remaining handed Walker the chance to knock over a penalty goal to make it 31-24 and from there the Roosters hung on to claim the valuable premiership points.
- Roosters skipper James Tedesco played his 100th game for the club.
- Mitch Moses has racked up seven try assists across three years of Magic Round.
- Jared Waerea-Hargreaves was placed on report in the 19th minute for a crusher tackle on Hayze Perham.
- The Roosters lost hard-working lock Victor Radley to an ankle injury in the first half.
- Leading from the front for the Roosters was Jared Waerea-Hargreaves in game No.270 with a try and 157 metres from 15 hit-ups.
- The Roosters have won six of their past seven games against the Eels.
- Isaiah Papali'i was a powerhouse for Parra with two tries, three tackle breaks and 166 running metres.
- Joseph Suaalii has scored five tries in his past three matches.
- Eels five-eighth Dylan Brown was placed on report for high contact on Sitili Tupouniua in the 73rd minute. The Roosters back-rower left the field for a HIA.
Plays of the Game
Following on from Adam Reynolds' sublime chip and chase try on Friday night, Roosters whiz kid Sam Walker produced some magic of his own in the 25th minute when he got the ball 25 metres out and nudged one over the top of the Eels line. With Clint Gutherson nowhere to be seen, Walker chased his kick and slid over to give the Roosters a dominant 20-6 lead. Still just 19 and 31 games into his career, Walker showed the composure of a man 10 years his senior to spot the opening and land the kick perfectly.
Anything you can do.... Mitch Moses answered Walker's brilliance with a try in the 50th minute that had the blue and gold contingent on their feet at Suncorp. Moses danced down the right sideline, kicked back inside as the cover converged, kicked the ball a second time and won the race to the rolling ball to get the Eels right back in the match.
What They Said
"I felt like Jared [Waerea-Hargreaves] and Joseph [Suaalii] set the tone in yardage with their carries. Jared had a heap by 20 minutes in and then Suaalii sparked the way that he carried the ball but then the toughness and the class he showed in that game for an 18-year-old is remarkable. He has walked in, he's dreamt about those hard areas a lot and he has taken them on board and he has good mentors in Teddy and Toops at the back there." - Roosters coach Trent Robinson
"Our start was poor. The games that we've lost this year, we've been beaten to the punch at the start of the game and we're waiting to see what the opposition is going to do but we need to go after the game at the start. I was happy that we had that fight in us in the second half but against good teams, you give them that much of a start on the scoreboard it's very hard to peg back." - Eels coach Brad Arthur
The Roosters will welcome Lindsay Collins back from suspension for a Saturday night showdown with the Panthers at the Sydney Cricket Ground.
The Eels have a five-day turnaround ahead of their clash with Manly at CommBank Stadium. Sean Russell has returned from a rib injury in NSW Cup and could be a chance for a recall while Maika Sivo is closing in on his return from a knee reconstruction.
Story first published on NRL.com