I may as well play devil's Advocate here. It's not hard since I believe there are a number of key caveats that can be made about the performance. Somebody has already asked the key question, "How could they produce this performance after the shambles on Saturday?" Part of the answer at least lies with the opposition. Anyone who watched the reserves last week would have seen Jagielka, Coleman, Anichibe and (I think) Rodwell all performing well below par against Liverpool's reserve (made up of kids and Doni), a game that ended 0-0 and was replete with wasted chances by Liverpool. You can imagine my surprise then when these (Clearly unfit) players suddenly showed up against Liverpool. Reading the Everton forums afterwards part of the reason they were so upset (as alluded to above) was because they felt that Moyes had at worst thrown the game with a view to winning the FA cup tie at the weekend, at best put out a weakened side in hope rather than expectation. Certainly there was strength on their bench and the derisory efforts by Everton on the night bear testament to the argument that this was an Everton reserve side that was unfit and lacking form. Compared to the psyched up Liverpool side they were far more unmotivated.
The second point to make was the time and space offered to the Liverpool midfield. Liverpool have struggled to impose a 442 on teams this year, usually being out-numbered in the middle and seeing a disconnect between the midfield and the frontline. As has been noted by others elsewhere, the dropping of Adam seemed to offer a better balance in the middle. Spearing (who did an excellent job of closing space on defence) was neat and tidy in possession, always making himself available for short passes and generally maintaining possession and moving the ball. To me he was fundamental to the victory (and my actual MotM) because his performance allowed Gerrard to move higher up the pitch and support the front two much more effectively. However, the reason that Spearing was able to perform this task was largely due to the fact that Everton also played two strikers allowing Liverpool a lot more room in the middle. The fact that Everton's strikers were so vastly inferior was the difference in the score line, but the platform for the victory was created by Spearing and Gerrard whose dominance, in turn, owed much to the formation and players selected by Moyes. In a normal game Moyes would have put out a five man (or even six man) midfield and nullified that dual threat.
The other point to make is that the weakest performers for Liverpool on the night (in a night with a lot of good performances and an overall good team spirit) were once again Downing and Henderson. Of course some will point to the couple of nice balls Henderson played, but he was also caught in possession a number of times in dangerous areas and offered very little support to Kelly, defensively (anyone remember him getting nutmegged in his own box?) Downing on the other wing was also hit and miss and put in a pretty anonymous performance, truth be told.
I don't want to be too negative, because there were a lot of positives to be taken from the game. The balance looked much better (though Henderson just is not a right winger) with the midfield much more dynamic than it has been of late. Spearing and Gerrard were excellent in combination, getting forward and backward exceptionally well. I think the big plus for me was Carroll who grew in confidence and stature before your eyes. He linked well withe Suarez and played some lovely one touch stuff. It was heartening to see ( a 50 yard, diagonal lofted ball to Downing was one truly quality moment, but the bit I enjoyed the most was his beating three men and surprising Dowd so much that he blew up and gave him a sympathy freekick). Enrique had his best game for the club yet I felt and after some shakey performances recently it was an excellent display. Kelly was also terrific (but I think we are looking at the new Carragher in terms of goal scoring).
So, overall, much to be pleased about, but it should be tempered with the knowledge that the opposition were unusually awful and dispirited for a derby, the question of 442 v 433 is still unanswered and some of the players that have under performed all season have still continued to do so. Set against that, a dynamic and energetic display, a better balanced side and some good performances from unexpected quarters. Finally, kudos to the manager, after expressing doubts after weekend on his ability to successfully adapt the side to the challenges of the modern game he once again showed a shrewdness and willingness to make changes where necessary and when necessary too.