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Birmingham slipped to their second successive defeat after losing 1-0 at Middlesbrough last week.
United, beaten on their two previous visits to Birmingham, always had a slight edge with Solano and Kieron Dyer their key players in midfield.
It was not a happy match for Birmingham as Darren Purse collected his fifth booking of the season and now faces an automatic suspension.
Birmingham found themselves under a heavy bombardment in the opening 15 minutes as Newcastle obviously attempted to atone for their indifferent start to the season.
Newcastle, who are on their Champions League travels in Italy next week, produced some promising attacks in which Lomana Lua Lua was prominent.
His clever flicks forced Birmingham into some desperate situations and the Midlands club had a lucky let-off when a Solano corner was flicked on by Andy O'Brien only for Nico Vaesen to make a fine reflex save.
Birmingham weathered the storm in fine style and eventually managed to swing into an attacking formation but it was from a deadball situation that Newcastle posed the first real threat.
Paul Devlin, a candidate for the Scottish international squad, blasted a free-kick straight at Shay Given and forced the Newcastle keeper to save again from the rebound.
Given proved his top flight quality with another smart save from Stern John when the Irishman netted another blistering shot.
Robbie Savage collected his fourth booking of the season in the 27th minute for an alleged trip on Nikos Dabizas who had cut across the Welsh international.
At that time Birmingham were struggling to regroup and Newcastle exploited the situation when they went ahead in the 34th minute with a swiftly executed move.
Alan Shearer began the move with a pass to Laurent Robert who then put Solano in possession to score with a raking right-foot shot past Vaesen to record a quality goal.
Danger man Lua Lua, should have increased Newcastle's lead but he could only put in a weak header which was easily saved by Vaesen.
The major difference between the two teams was the speed with which Newcastle switched from defence to attack.
But white haired manager Sir Bobby Robson was far from happy with his side's inability to build on their lead as Birmingham slowly worked up a head of steam in the second half as they went in search of an equaliser.
In the end it was Newcastle who were forced to hang on as they lost all their previous poise and confidence.
The bustling substitute Geoff Horsfield ruffled a few feathers but Newcastle held on for three valuable points and in the 88th minute Ameobi sealed the match when he scored at the second attempt following a pass from Shearer