The Magpies went a goal down at Seoul World Cup Stadium, with Brennan Johnson's deflected drive giving Thomas Frank's men an early lead.
But Newcastle fought back and levelled before half time thanks to a trademark effort from Barnes, and they will have been satisfied with their work against their Premier League rivals.
Howe was able to introduce Lewis Hall from the bench in the closing stages after his lengthy absence through injury, while there were promising displays from a handful of his other charges as preparations for the start of the Premier League season in under a fortnight continue.
Spurs started at pace, with Pape Matar Sarr forcing Nick Pope to repel his drive after Mathys Tel's corner wasn't cleared. In the fourth minute, they went ahead. Jacob Murphy was robbed of possession in his own half and Spurs moved quickly, with Johnson picking it up and whipping a low shot - which took a deflection off Dan Burn - beyond Pope.
United responded to the early setback positively, with Anthony Gordon looking lively in attack. His cutback found Joelinton, who just couldn't quite connect decisively with it in front of goal, before Fabian Schär's swerving effort from range cleared the crossbar.
Gordon then hit the sidenetting from Murphy's lay-off before Pope was called into action again at the other end. Tel somehow escaped punishment for appearing to fell Matt Targett on halfway, leaving the Frenchman with a clear run through on goal. He took his time and tried to make Pope commit, but the Magpies' stopper did brilliantly to read the forward's intentions and throw out a leg to block the shot.
Joelinton glanced Bruno Guimarães' cross just wide and Pope tipped a vicious Pedro Porro free kick over the bar, but seven minutes before the break United pulled themselves level. Gordon was involved again, leading a breakaway down the middel before feeding Barnes on the left. He cut inside Porro onto his favoured right foot, as he does so well, and sent a powerful finish past Antonín Kinský and in off the Spurs stopper's right-hand post.
After the restart, the impressive Gordon sidefooted a Targett cross wide of the upright. He could have snatched himself a deserved goal, too, when he met Murphy's inviting inswinging centre in the box. The former Everton man's volleyed finish was confident and unerring, but the strike was chalked off for offside; Gordon was a yard or two the wrong side of his man when Murphy provided the assist.
With just over an hour gone, Gordon was withdrawn, with Will Osula sent on to provide an alternative attacking threat. Tino Livramento replaced Targett as well before Spurs hero Heung-min Son was replaced on what will likely be his final game for the club amid emotional scenes in his home country.
Lucas Bergvall forced a relatively straightforward save from Pope, but the Magpies custodian - who had turned in a solid display - then had to prevent substitute Richarlison from winning it for Spurs. Wilson Odobert's trickery created the opening for the Brazilian, who shot low across goal - but Pope saved well again, getting a foot to it to divert it wide.
It will have been encouraging for Howe and the Magpies' faithful to see Hall back in action after a lengthy spell out with injury, with the full back entering the fray for the final quarter of an hour, while there were also cameos for youngters Seung-soo Park and Travis Hernes as United brought the curtain down on their trip to South Korea.
Newcastle United: Nick Pope (Mark Gillespie 82); Kieran Trippier (Lewis Hall 77), Fabian Schär (Emil Krafth 82), Dan Burn, Matt Targett (Tino Livramento 61); Bruno Guimarães, Lewis Miley, Joelinton (Travis Hernes 86); Jacob Murphy (Seung-soo Park 77), Anthony Gordon (Will Osula 62), Harvey Barnes (Anthony Elanga 82).
Subs not used: Odysseas Vlachodimos, John Ruddy, Max Thompson, Harrison Ashby, Jamaal Lascelles, Alex Murphy, Sandro Tonali, Alfie Harrison, Sean Neave.
