The visitors have started well in North London, with Anthony Elanga instrumental in forcing a couple of early corners before crossing for Botman to head over.
Xavi Simons dragged a shot through Kieran Trippier's legs and into the sidenetting for the hosts, but Joe Willock went even closer for the Magpies, firing just wide of the target after some neat build-up play involving Harvey Barnes, Anthony Gordon and Bruno Guimarães.
Head coach Eddie Howe made four changes to his side for the trip to the capital, with Dan Burn, Jacob Ramsey, Elanga and Gordon coming into the starting 11 at the expense of Lewis Hall, Sandro Tonali, Jacob Murphy and Yoane Wissa.
Newcastle United: Nick Pope; Kieran Trippier, Sven Botman, Anthony Gordon, Harvey Barnes, Malick Thiaw, Anthony Elanga, Joe Willock, Dan Burn, Bruno Guimarães (c), Jacob Ramsey
Substitutes: Aaron Ramsdale, Lewis Hall, Sandro Tonali, Yoane Wissa, Will Osula, Jacob Murphy, Nick Woltemade, Alex Murphy, Leo Shahar