Rondon netted twice in a 2-1 win over Bournemouth at St James's Park.
The on-loan striker put in a superb all-round performance and the result, United's second successive victory, moved the club up four places ahead of the international break.
There was a minute's silence before the game ahead of Remembrance Sunday. There was a stunning display of poppies in the Gallowgate end of the stadium.
The XI that finished last weekend's game against Watford started the fixture. Fabian Schar, Ki Sung-yueng and Ayoze Perez replaced Jamaal Lascelles, Jonjo Shelvey and Yoshinori Muto respectively.
Newcastle started well, though they had Federico Fernandez to thank for an early block which stopped a shot from Jordan Ibe.
Their breakthrough came in the seventh minute when DeAndre Yedlin got behind the visisting defence and delivered the ball to Rondon, who scored past Asmir Begovic at the second attempt.
Bournemouth fought back, and United goalkeeper Martin Dubravka did well to palm away a Ryan Fraser free-kick.
Eddie Howe's team lost momentum during a lengthy stoppage for treatment to Adam Smith, who was replaced by Charlie Daniels, and Rondon put Newcastle 2-0 up in the 40th minute with a powerful header.
Ki played a superb cross-field ball for Kenedy, whose left-wing cross was nodded past Begovic by the 29-year-old.
United, however, didn't take their two-goal advantage into the break. Six minutes into stoppage time, Jefferson Lerma headed home a cross from Fraser.
Bournemouth pressed hard for an equaliser in the second half, and Benitez sent on Isaac Hayden and Ciaran Clark to shore up his team. Christian Atsu followed them on to the pitch.
Benitez switched to a five-man defence late in the game, and former Newcastle midfielder Dan Gosling had a goal chalked off for offside.
And United saw the game out to go into the international break on a high.
NEWCASTLE UNITED: Dubravka; Yedlin, Schar, Fernandez, Dummett; Ki, Diame; Ritchie (Hayden, 74), Perez, Kenedy (Clark, 78); Rondon. Subs not used: Darlow, Murphy, Manquillo, Joselu.
BOURNEMOUTH: Begovic, Francis, Cook, Ake, Lerma (Gosling, 46), Ibe (Defoe, 81), Wilson, Smith (Daniels, 30), Cook, Brooks, Fraser. Subs not used: Boruc, Surman, Pugh, Mousset.
Goals: Rondon 7, 40, Lerma 45
Bookings: Schar 45, Cook 90, Rondon 90
Referee: Lee Probert (Wiltshire)