Without his main strike force, caretaker boss Glenn Roeder stretched his unbeaten run to five games of which there have been four victories and four clean sheets for usually much-maligned back-four.
Solano pounced after 64 and 76 minutes, the first seeing the talented Peruvian take his tally in English football to the 50 mark.
The omens were there after Solano's opener as now in the12 times they have scored first this season United have never lost, winning ten and drawing the other two.
With a strong wind behind them, Everton controlled the first half as twice David Weir from similar corner kick routines saw headers cleared off the line by Emre.
Then in time added on, Sander Westerveld marked his debut with a stunning close-range save from Solano to prevent United going in front at the interval.
Shay Given in between pulled off an excellent save from a Mikel Arteta free-kick.
Emre had earlier played a pivotal role in attack when a clever run and cross evaded the unmarked Shola Ameobi who then blotted his copybook when he failed to control the ball when put in by the little Turk.
On the quarter-hour mark, United's resilience in defence was further emphasised when Jean Alain Boumsong cleared from Kevin Kilbane's cross to the back post.
Aussie Tim Cahill was cautioned after 39 minutes and could easily have seen red when he tripped Lee Bowyer, but referee Graham Poll chose to take no action on the second occasion.
Leon Osman got on the blind side of Boumsong to lash the ball behind before United broke the deadlock after 64 minutes.
The determination of Charles N'Zogbia was the decisive factor. The young Frenchman raced 30 yards as Emre held up the ball and skipped past the static Weir before drilling over a cross that saw Solano beat Nuno Valente to force the ball over the line.
Westerveld pulled off a brave save to deny Lee Bowyer at the expense of a corner that Scott Parker volleyed wide.
Aware of the importance of a second goal, United achieved that target after 76 minutes when Solano scored with the most delightful of right-footed curlers after being picked out by Bowyer.
This was only the third time this season that Newcastle had scored more than two goals in a home match and the fans loved it.