Solanke blasted home on 60 minutes to open the scoring before doubling his tally 13 minutes later to earn the points for Bournemouth, who could have scored more against a depleted United side.
Former Cherries boss Eddie Howe lost another key member of his squad, Miguel Almirón, in the first half as Newcastle's injury problems worsened on a day to forget on the South Coast.
In a tight first half, the hosts made sure Nick Pope was the busier goalkeeper. He was forced to save from Ryan Christie within the first minute and while Sean Longstaff made Neto make a similarly important stop soon after, it was the Cherries who were asking the majority of the questions. Only a superbly-timed, last-ditch block from Jamaal Lascelles stopped Solanke from pulling the trigger in the box early on.
Justin Kluivert had a go too, stinging Pope's palms with a drive from distance after breaking from midfield, and before the break United suffered another injury blow as Miguel Almirón - restored to the side in one of three changes made by Eddie Howe - was withdrawn early, with Matt Ritchie sent on to replace him. Almost immediately after the change, Pope got down well to turn away Christie's bouncing strike and Antoine Semenyo then sidefooted a Solanke lay-off just past the post as Bournemouth rallied.
Tino Livramento was sent on at half time as the Magpies looked to limit the effectiveness of the lively Semenyo but a weak backpass from Kieran Trippier almost allowed another frontman, Solanke, a chance to round Pope shortly after the restart, but it was a chance he couldn't take as his control failed him as he looked to pounce.
The visitors almost snatched the lead when Trippier's inswinging delivery bounced off Neto, who then got himself in the way of Solanke's attempted clearance which cannoned back his way off Joe Willock.
But just before the hour, Solanke struck, latching on to a loose ball behind the United backline and drilling home past Pope at the near post. It was a goal which, in truth, Andoni Iraola's men deserved, but it owed much to an unfortunate touch off Willock, which allowed Solanke the chance to run onto it and put his team ahead.
Anthony Gordon tested Neto again and Ben Parkinson was brought on for his Premier League debut just as another youngster, Lewis Miley - on his first top flight start - was taken off. But still it was the Cherries who carried the biggest threat, and with just under 20 minutes remaining they made sure of the points. Ritchie inadvertently diverted a corner onto his own post and Solanke reacted quickly, improvising to flick home from close range with the outside of his foot.
Sean Longstaff had a chance to pull one back for the Magpies moments later, but he couldn't keep his shot down and the hosts' two-goal advantage remained intact - and could even have been extended late on as Solanke and, on multiple occasions, Luis Sinisterra went close in the closing stages - on what was a miserable return to the Vitality Stadium for Howe and his charges.
