The on-loan Manchester United forward nodded the Catalan giants into the lead at St. James' Park before thumping home a superb second after the hour to extend their advantage.
There was to be no repeat of Tino Asprilla's 1997 hat-trick heroics for United, who faded after the restart against an impressive Barça outfit.
They remained in the contest right to the end though with Anthony Gordon pulling one back in the 90th minute to spark hopes of an unlikely comeback, but it wasn't to be for United on matchday one in Europe's top competition.
Buoyed by the deafening atmosphere, United set about unsettling the visitors, who played dangerously at times with goalkeeper Joan García doing well to evade some intense pressure from the hosts' forward line early on. Anthony Elanga's cutback was perfect for Gordon, who missed his kick, while Harvey Barnes tested García with a low curler after a one-two with Sandro Tonali.
But LaLiga's reigning champions looked typically threatening in attack. Rashford turned his former England teammate Kieran Trippier on halfway and set off for goal before scuffing wide, while defender Jules Koundé sliced over the bar after veteran frontman Robert Lewandowski had beaten Nick Pope to Rafinha's inswinging centre.
The best chance of the half, though, was created by Howe's men. Captain Bruno Guimarães timed his through ball to perfection and released Elanga on the right, with the Swedish winger's cross leaving Barnes with a great opening. But García did well to block the winger's finish, turning it away at his feet from close range.
Hansi Flick's side began to turn the screw a little towards the end of the half, with Rafinha finding the sidenetting at the end of a dominant few minutes for Barça, but Newcastle restarted with intensity after the break. Barnes' industry won them a corner and Joelinton glanced it wide, while Rashford took aim again at the other end and finding Fabian Schär in the way.
Tonali then drove straight at García from range but just before the hour, Rashford opened the scoring. Koundé's inswinger found him in space in the box and his header bounced beyond Pope below the small band of travelling fans who had made the trip to Tyneside.
Fermín López tried his luck soon after but once more found Schär blocking the shot just before the Swiss defender was withdrawn as part of a quadruple substitution from Howe which saw Nick Woltemade, Jacob Murphy, Joe Willock and Malick Thiaw introduced.
The Magpies had lost a little rhythm in the second half and their hopes were punctured again by Rashford's terrific second on 66 minutes. It was a eyecatching strike, crashing in off the crossbar from 20 yards, and it left the hosts with an even steeper climb ahead against slick opposition.
Brazilian international Rafinha cut inside and flashed an effort past the post on the counter and though Guimarães had an attempt after a good run from Gordon and a neat flick from Woltemade, Gordon's last-minute goal - rolled home at the Gallowgate End from Murphy's pinpoint cross - failed to herald a late reprieve for United, who began the league phase with defeat.
