The little Peruvian smashed in his first goal at St James' Park in 30 months to make it four wins out of five at home for beleaguered Graeme
Souness.
Arsenal had been unbeaten in their previous eight league encounters in these clashes, the Gunners winning six with the other two drawn.
However, the crest-fallen Gunners did not help their own cause despite dominating the first 45 minutes after which they left Newcastle off the hook.
Fresh from their 2-0 defeat at Bolton, Arsenal were forced to play the final 33 minutes a player short after Brazilian Gilberto was yellow-carded twice in 12 minutes by referee Dermot Gallagher and sent off.
Newcastle had already stepped up a gear in the second half, the departure of Gilberto moved them into overdrive.
While Arsene Wenger bemoaned the red card, he appeared to forget the corresponding fixture at Highbury earlier in the season. That was when Jermaine Jenas was sent off when it was goalless - a decision later overturned – and the Gunners won with two late goals.
Solano's winner was the 200th league goal that Arsenal has now conceded against United in 146 encounters while in comparison, Newcastle have now scored 215.
Despite their horrendous injury situation, Newcastle were given a boost when they saw Michael Owen return after missing the last four games.
But the first half clearly belonged to the Gunners whose fast and flowing passing game frequently tore Newcastle to shreds.
Alexander Hleb was outstanding on the left and the Thierry Henry trickery was a pleasure to watch. Yet, and despite their superiority, the Gunners managed only one shot on target as Henry was brilliantly denied by Shay Given.
Another top quality performance from Parker saw him produce United's only worthwhile first-half effort which was easily handled by Jens Lehmann.
That was after 13 minutes with the Gunners feeling they were denied a penalty 60 seconds later.
Henry won a right-wing corner that saw Gilberto's powerful header blocked and when he drove in the rebound the ball did strike the hand of the unaware Titus Bramble.
The Arsenal first-half opportunity that should have been put away, came after 27 minutes. Cesc Fabregas whipped in a great cross that Henry volleyed goalwards only for Given to claw the ball away.
Fabregas and Henry then wasted other chances before Faye was cautioned five minutes before the break for a foul on Phillipe Senderos and on the stroke of the whistle there was a decisive yellow for Gilberto following a rash lunge on Shola Ameobi.
A rejuvenated United started with style after the break as Parker drove over and Shearer went within inches of breaking the deadlock.
A Jean-Alain Boumsong drag-back saw his standing leg taken away by Gilberto and he was quickly sent to the dressing room.
Lifted by that, United went for the win with some style. Lehmann put Hleb under pressure with a throw out from a corner and with the keeper out of his goal Parker again went close.
A great run from Kolo Toure – about all Arsenal offered in the second half – saw the ball pulled back to Robin Van Persie on the edge of the box, but his air-shot just about summed up Arsenal's woes.
Parker needed lengthy treatment after colliding with Lehmann. The work-horse midfielder lost a tooth and was later helped from the field with concussion.
Lee Bowyer was thrown on and produced a no-nonsense display as Newcastle stormed ahead eight minutes from time.
Shearer did the bulk of the spadework as the ball was powered to his feet on the left of the area. He somehow maintained possession and crossed for Solano to control and rifle a lot shot across Lehmann and into the back of the net.
The icing on the cake almost followed when Peter Ramage – solid in defence – launched the ball forward and Owen at full stretch controlled but could not supply the killer touch.
The little striker ran his heart out before fitness told in the dying seconds and he made way for Michael Chopra.
Newcastle are now just four points adrift of Arsenal. Saturday sees them at West Ham before a Boxing Day date for Owen against Liverpool at Anfield before the curtain comes down at St James' Park this year against Charlton.
MAN OF THE MATCH: Jean-Alain Boumsong (Newcastle) - Seems to relish his displays against his French national team-mate Thierry Henry. Rock solid in his best display of the season.