Kuyt set the visitors on their way to three Premier League points at the Stadium of Light on Sunday with 33 minutes gone when he converted a hotly-disputed penalty, and Suarez completed the job with 13 minutes remaining.
But the Black Cats trudged off the pitch on the final whistle hugely aggrieved at the penalty decision with John Mensah, who was later shown a straight red card for a professional foul on Suarez, clearly tripping Jay Spearing outside the box.
However, while they may have had reason to feel hard done by, Steve Bruce’s men were rarely a threat despite enjoying the greater share of possession, and Reds goalkeeper Pepe Reina did not have a save worthy of note to make until he plucked Lee Cattermole’s long-range effort out of the air four minutes from time.
Liverpool were much more effective despite £35million man Andy Carroll enduring a quiet afternoon on his full Premier League debut for the club, and home goalkeeper Simon Mignolet had to pull off good saves from Kuyt, Suarez and Spearing to keep the scoreline respectable in front of a sell-out crowd of 47,207.
Sunderland went into the game having ended a run of four consecutive league defeats with a hard-earned point at Arsenal a fortnight ago, and with Danny Welbeck back in the starting line-up and skipper Cattermole on the bench after injury, there was genuine optimism on Wearside for a repeat of last season’s victory over the Reds.
That day, of course, they enjoyed the most outrageous slice of good fortune when Darren Bent’s shot found its way into the back of the net with the help of a deflection off a beachball.
This time around, they had plenty of luck, but all of it bad.
By the time 22 minutes had elapsed, Bruce had been forced to use two of his three substitutes as first Sulley Muntari and then Kieran Richardson limped off.
To their credit, the home side were not unduly affected as Cattermole, playing for the first time since December 28, and Steed Malbranque were drafted in and Stephane Sessegnon and Welbeck particularly lively.
However, despite enjoying the better of the possession, the Black Cats created little of note before the break with Welbeck’s 17th-minute cross from the left which just eluded Richardson as close as they came to troubling Reina.
By contrast, the visitors struggled to get the ball anywhere near Carroll and Suarez, the latter of whom spent much of his time wide on the right, where he was largely effectively shackled by full-back Phil Bardsley.
However, it was they who created the better opportunities with Kuyt the main beneficiary.
Simon Mignolet bravely blocked the Dutchman’s fifth-minute shot at point-blank range after Carroll had headed down Raul Meireles’ corner, and Kuyt headed over from the resulting set-piece.
It was he who eventually broke the deadlock, but he did so in controversial circumstances.
Mensah’s poor control allowed Spearing to burst towards the penalty area, and the Ghana international brought him down in his efforts to make amends.
Replays showed the initial contact had taken place outside the area but referee Kevin Friend pointed to the spot on the advice of his assistant.
Kuyt sent Mignolet the wrong way to give the visitors the lead, and it might have been 2-0 before the break had the Belgian not got down well to palm away Suarez’s well-struck 37th-minute effort.
Malbranque miskicked when presented with a 48th-minute half-chance after Jordan Henderson had worked a short corner move with Anton Ferdinand as Sunderland started the second half brightly.
However, the game might have been over three minutes later had Cattermole not managed to block Carroll’s header on the line with his knee after the striker had been allowed to meet a Meireles corner unmarked.
The same pair could have put the result beyond doubt with 54 minutes gone when, after Mr Friend had allowed play to continue when Titus Bramble felled the striker, the midfielder fired over the top.
There was fury inside the Stadium of Light when the official then awarded the free-kick, which Suarez curled just wide.
Substitute Ahmed Elmohamady saw a header and then a follow-up shot blocked from Jordan Henderson’s 65th-minute corner, but the points were safe with 13 minutes when Suarez squeezed his way into the box and blasted past Mignolet from a seemingly impossible angle.
A bad day for the Wearsiders took a further turn for the worse with 81 minutes gone when last man Mensah hauled Suarez down and was promptly shown a straight red card.