Alonso struck in the ninth minute when his 20-yard shot deflected off Jose Bosingwa and left Petr Cech wrong-footed.
It was Chelsea's first defeat under new boss Luiz Felipe Scolari. Chelsea had not been beaten at home since Arsenal's 2-1 success in February 2004 but Liverpool deserved their triumph with an impressive display.
Chelsea began the brighter of the two sides and their initial thrusts almost resulted in an opening goal.
Nicolas Anelka dribbled his way into the penalty area in the third minute but was tackled before he could test Jose Reina.
The ball fell to Deco but the Chelsea midfielder's shot was deflected to safety.
Liverpool went ahead in the ninth minute with their first attack of the game.
Chelsea failed to deal with a thrown-in when John Terry could only half-clear Dirk Kuyt's clever back-header.
The ball fell to Alonso on the edge of the penalty area and his shot deflected luckily off Chelsea right-back Bosingwa into the net.
In the 17th minute, Albert Riera beat Bosingwa on the left flank but fired his shot into the side netting.
Chelsea, hoping to stretch their unbeaten home league sequence to 87 games, struggled to get back into the game.
Bosingwa tried to run at the Liverpool defence in the 21st minute but was chopped down crudely by Riera who received a deserved booking from referee Howard Webb as a result.
Seconds later Salomon Kalou headed just over the bar from another cross by Bosingwa.
Liverpool continued to look dangerous and in the 24th minute they almost increased their lead when Cech was forced to tip a glorious volley from Ickle Steven Gerrard over the bar.
Chelsea began to find some consistency as the first half wore on but they were struggling to produce a telling final ball into the penalty area.
Time and again their neat approach work was undone by a poor pass but Frank Lampard, so often their inspiration, won a corner in the 33rd minute with a deflected shot.
But although it came to nothing, Chelsea continued to enjoy their best spell of the game.
Bosingwa sent over a number of crosses from the right flank but Daniel Agger and Jamie Carragher, through a process of undetected holding and shirt pulling, managed to survive.
In the 36th minute Deco was given time and space to run at the Liverpool defence but his left-foot drive from 18 yards was wide of Jose Reina's right-hand upright.
In the 38th minute Gerrard should have been heading for an early bath for a foul on Bosingwa.
However, referee Webb elected to show the media's golden boy a yellow card for his challenge.
Liverpool's speed on the counter-attack almost opened up Chelsea again in the 43rd minute but, despite some confusion in the home defence, John Mikel Obi managed to clear their lines.
Chelsea began the second half in a much brighter fashion and it required an interception from Carragher to prevent a cross from Florent Malouda reaching its destination in the six-yard box.
In the 53rd minute Malouda was booked for checking a fine run by Alvaro Arbeloa.
Moments later Malouda was felled by Liverpool 'keeper Reina in the penalty area but he had already been ruled offside by referee Webb.
Cole was next into Webb's book when the official took a dislike to his challenge on Carragher.
In the 57th minute, Kuyt tried his luck from 20 yards but his effort was wide of the target.
It was the catalyst for a Chelsea to make a double substitution with Malouda and Kalou replaced by Juliano Belletti and Franco Di Santo.
It was another indication of Chelsea's growing frustration and it prompted Liverpool to replace Robbie Keane with Ryan Babel.
The Reds were awarded a free-kick 25 yards out in the 60th minute when Belletti kicked Riera in the face.
Chelsea then had a massive escape when Alonso's effort rebounded off the foot of the post for Ricardo Carvalho to clear.
Babel was brought down by Cole as he tried to collect the ball but referee Webb decided, quite rightly, to book Javier Mascherano for attempting to persuade the official to dismiss the left-back.
Cole squandered a great chance to level the scores in the 73rd minute when Di Santo nodded Lampard's cross into his path.
But the defender screwed his effort wide of the post from eight yards. Moments later Carragher rescued Liverpool when he deflected Deco's effort for a corner.
At the opposite end, a 25-yard drive from Babel was only just wide of the target.
All in all, the standard of Howard Webb's refereeing was awful to say the least and if he's supposed to be the best we've got then refereeing in the Premier League is in serious trouble.
Although Liverpool shaded the game performance wise, and that's debateable, their last two games were won with late comebacks, one of them against ten men and they got a lucky deflected goal against us, which the wrong footed Cech would have saved comfortably otherwise, so I still can't see them being up there at the end of the season.
Having said that, we looked pretty lightweight up front and I think Anelka just isn't good enough for us. We need Drogba back and maybe a forage into the transfer market in January for another striker but I still think it'll be us and United again in May.