Walcott, who had not netted a competitive goal for the Gunners since April, pounced in the 25th minute to make it 1-0 at the Emirates and at that stage it looked as though Arsenal would steamroller their League One opponents.
Despite a glut of first-half chances the hosts failed to extend their lead and Doncaster, having frustrated Olivier Giroud as he sought his 100th goal for Arsenal, probed for an equaliser and gave the Premier League side a number of scares.
Darren Ferguson’s men lacked quality in the final third and the few clear-cut chances they created went begging, leaving Arsene Wenger to reflect on a positive result and another good performance from Jack Wilshere.
The midfielder, who spent last season on loan at Bournemouth, made his first start for the club since May 2016 and was involved in much of Arsenal’s best play, while full-back Reiss Nelson also emerged with credit on his full debut.
A lively opening four minutes saw Doncaster winger Rodney Kongolo draw a diving save from David Ospina with a low drive, before Giroud had a strong claim for a penalty turned down when the referee refused to acknowledge that he was hauled down in the penalty area.
The Frenchman almost scored a contender for goal of the competition two minutes later when he met Wilshere’s delicately chipped ball into the box with an acrobatic scissor-kick that beat Ian Lawlor but rattled the crossbar.
Giroud headed a pinpoint Mohamed Elneny cross narrowly over the crossbar after 20 minutes as Arsenal camped themselves in Doncaster’s half, with Wilshere and Nelson moving the ball around crisply.
The breakthrough arrived after 25 minutes when Alexis Sanchez looped the ball into the box and behind the Doncaster defence where Walcott arrived and took a touch to control before side-footing it past Lawlor and into the net.