They are the only Welsh side left in European competition and - should they win the tournament - it will mean all four Welsh regions qualifying for next season's Heineken Cup.
With the Falcons having their Guinness Premiership survival campaign on their mind, the Blues had said they expected a dour, forward-oriented game on a sticky pitch.
But a disappointing crowd of 4,346 at the Kingston Park Stadium enjoyed a free-flowing start in the Tyneside sun.
Blues centre Laulala slipped through a nervous Falcons defence after Richie Rees broke from a short-range scrum for the opening score on 10 minutes.
Jimmy Gopperth, the leading scorer in the Amlin this season, replied with a penalty following a Blues ruck offence in the shadow of their posts.
Ben Blair contributed 20 points with the boot and a second-half try
The visitors were showing admirable attacking intent, stretching the Falcons from one side of the pitch to the other, and were rewarded for a Sweeney break when Williams stretched out from the back of a ruck for the second try.
Despite the apparent Blues domination, the Falcons - missing captain Carl Hayman after a late back injury withdrawal - were seizing every chance that came their way.
Williams and Deiniol Jones looked to have wrapped up an attempted break by Amesbury, but, as the forwards went to rip the ball from the Falcons player's grasp, the wing burst free to sneak in under the posts.
Gopperth converted, then cut the deficit to a single point with his second penalty.
Blair cancelled that out with a kick to make it 17-13, a narrow Gopperth miss on the stroke of half-time ensuring it stayed that way at the break.
The visitors re-emerged determined to make their apparent superiority tell on the scoreboard, the forwards keeping it tight as Xavier Rush and Bradley Davies rumbled upfield for Filise to profit with his first try.
Taufa'au Filise's two tries delighted Blues lock Deiniol Jones
Blair converted and soon added a penalty to stretch the lead to 14 points.
The advantage established, the Welsh side began to open out again, a Filise break paving the way for the ball to be spread wide by Williams, Blair the man to profit from a huge overlap with his side's fourth try.
Gopperth hoped to get Newcastle back on track after a fine break, off-loading when he heard a call inside.
But, to the fly-half's fury, the shout was from Blues captain Paul Tito, who gleefully took possession and set off an attack that led to Roberts crossing for the fifth try.
Filise notched his second try as the home defence disintegrated, but the Falcons finally gained some consolation when Young spotted a gap from a ruck to sneak over for a try converted by Gopperth.
The Blues blasted past the 50-point mark in the closing minutes, though, an electric Leigh Halfpenny break setting up Sweeney for the closing score.
Newcastle director of rugby Steve Bates: "I thought the first half was one of the best halves we have played all season.
"We coped well against an outstanding Cardiff team and in that first half we defended well and attacked pretty well.
"They had a couple of extra gears in them and we couldn't match that after half-time, especially after playing three games in a week last week.
"They are a quality outfit and you have to be at the top of your game, and we just fell off it a bit in the second half."
Blues director of rugby Dai Young: "Our message at half-time was just to tighten things up a little as we were just trying to force the final pass when we didn't need to. The opportunities then came and we took them.
"We have scored 88 points in the last two away games and that is a good thing in anybody's book, but we are keeping our feet on the ground.
"Things went for us, I think the odd bounce of the ball went our way, but we did play well.
"We have got a huge game against the Scarlets coming up. It's a do-or-die game for them and it's hugely important for us as well.
"If we win we will secure our Heineken Cup spot and I am sure the Scarlets will be very up for this fixture."
Newcastle: A. Tait, Biggs, Bobo, Tu'ipulotu, Amesbury, Gopperth, Young, Golding, Vickers, Ward, Hudson, Levi, B. Wilson, Williamson, Afu. Replacements: Catterick for A. Tait (46), Micklewood for Amesbury (64), Pilgrim for Young (66), Shiels for Golding (58), Walker for Vickers (68), Brooks for Ward (52), Sorenson for Hudson (45), Welch for Williamson (56).
Blues: Blair, Halfpenny, Laulala, J. Roberts, Czekaj, Sweeney, R. Rees, Jenkins, T. Thomas, Filise, B. Davies, D. Jones, Molitika, M. Williams, Rush. Replacements: Flanagan for Laulala (70), Hewitt for J. Roberts (61), D. Allinson for R. Rees (56), Yapp for Jenkins (56), G. Williams for T. Thomas (46), Andrews for Filise (61), Tito for B. Davies (52), Warburton for Rush (68).
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