Visiting Rovers began this all-Premier League affair the brighter side and opened the scoring in the 35th minute. Having opened his account for the club last week, striker David Goodwillie turned the ball in from close range following a goalmouth scramble.
Goodwillie had a good chance to extend his side's lead in the 68th minute but his effort from the edge of the box went wide of Tim Krul's goal.
Newcastle punished that miss just one minute later courtesy of Hatem Ben Arfa. The Frenchman collected possession just inside the Rovers half, before embarking on a weaving run past five visiting defenders. With just Mark Bunn in goal to beat, the midfielder kept his composure to slot in from close range.
Just as it looked as though Rovers had earned a replay, Argentine winger Gutierrez cut in from the left to shoot past Bunn and win the tie for the Magpies.