Coventry were awarded a penalty in the opening stages of the league encounter as Magpies goalkeeper Lukáš Horníček brought down Sidiki Cherif inside the penalty area before Rudoni converted from 12 yards, sending the Czech goalkeeper the wrong way in the process.
After the early setback, Newcastle went in pursuit of a leveller as Matias Fernandez-Pardo, targeting a first Magpies goal since last summer's move from Ligue 1 side Lille, missed a key opportunity to draw Newcastle level.
Jacob Murphy's inviting low cross from the right flank found the Belgium international inside the box but the unmarked attacker dummied the ball, with no Magpies player on hand to attempt an effort at goal.
United went agonisingly close to equalising on the stroke of half-time as Fernandez-Pardo raced onto Nico González's through ball but, despite rounding City goalkeeper Carl Rushworth, the Brussels-born forward saw his goal bound shot blocked on the line by Bobby Thomas.
Newcastle take on Coventry in an English top-flight encounter for the first time since January 2001 as goals from Gary Speed, Shola Ameobi inspired the Magpies to a 3-1 victory at St. James' Park.
United target an eight successive win against the Sky Blues and have suffered just one defeat in their last 13 meetings.
**Newcastle United:** Lukáš Horníček, Lewis Hall, Sven Botman, Nico González, Yoane Wissa, Harvey Barnes, Malick Thiaw (c), Matias Fernandez-Pardo, Jacob Murphy, Joe Willock, Lewis Miley.
**Subs not used:** Nick Pope, Fabian Schär, Joelinton, Aladji Bamba, Will Osula, Sean Steur, Bazoumana Touré, Dan Burn, Amar Dedić.