The Spaniard's sublime effort 11 minutes from time was his second from behind the halfway line in his short Liverpool career and surpassed his previous best against Luton, sailing over a desperate Steve Harper in the Newcastle goal to ruin his first league start for the Toon since April 2005.
But despite the euphoria surrounding Alonso's moment of class, Rafa Benitez will have been concerned to see his side once again struggle to convert a hatful of chances against a very ordinary looking Newcastle side.
Kuyt's opener on 28 minutes was the highlight in an otherwise uneventful first half, with Liverpool seemingly happy to pass the ball around the midfield and Newcastle content to let them.
Harper, in for the injured Shay Given, made two good saves from Craig Bellamy and Luis Garcia in the first 20 minutes, but Liverpool seemed to lack the killer instinct that despatched so many teams at Anfield last term.
Just as it seemed that Benitez's boys were running out of ideas, Alonso's incisive reverse pass split the Newcastle defence and allowed Steve Finnan to put it on a plate for Kuyt, the Dutchman sliding in from five yards to dink the ball past Harper.
Anfield erupted and the new boy's elation was matched by Benitez's relief that someone had finally managed to put an end to a worrying 298-minute drought.
Newcastle came out in the second half with a renewed sense of purpose and Shola Ameobi had an early shout for a penalty waved away after he had wriggled free of the excellent Dan Agger, but fell rather easily inside the Reds' box.
Kuyt should have doubled his haul five minutes into the second period. Garcia's clever run down the left drew four Newcastle defenders and his cut back found the ex-Feyenoord player open 12 yards out.
But he failed to connect properly and sent a mishit right-footed effort dribbling disappointingly wide. Seconds later Ameobi had a second penalty claim turned down, this time firing a wicked left-footer seemingly on to Jamie Carragher's hand.
Bellamy endured a torrid night under the constant barracking of the Toon faithful, still angry at his acrimonious departure from St James' Park and the subsequent bating of club hero Alan Shearer.
On 56 minutes it got worse for the Welshman. Peter Ramage's clearance was charged down by Steven Gerrard and fell invitingly into Bellamy's path. His pace took him past Craig Moore, but with the goal at his mercy he chipped the ball over Harper but wide of target.
Garcia almost added a spectacular second, taking down Gerrard's long ball superbly and firing a left-footed volley past Harper in one motion only for the post to deny him.
But if that effort was sublime, Alonso's was quite ridiculous. After winning the ball on the edge of the halfway D he turned, spotted Harper off his line and unleashed a wickedly accurate drive that forced the Anfield crowd to its feet.
Scrambling back the Newcastle keeper stumbled and the ball bounced on the line before the net bulged and the home supporters went wild.
Late on Momo Sissoko wasted a good headed chance and Bellamy shot over from close range.