The Gunners laboured to a narrow victory, which left more questions than answers over life after Cesc Fabregas.
Boss Arsene Wenger - who watched from the stands as he served a touchline ban - had called for a response from his young squad following the sale of their captain back to Barcelona.
It seemed he would get just that when Walcott, under the watchful eye of England boss Fabio Capello, swept the home side in front after only four minutes.
However, from then on, Arsenal never really got into any sort of rhythm as Udinese grew into the game.
Indeed, the Italians will feel frustrated the industry of captain Antonio Di Natale did not bring them an away goal to take back to the Stadio Friuli next week.
Before then, the Gunners must regroup for the visit of Liverpool on Saturday, when they will again face a stern examination of whether they can indeed go on to challenge for honours.
It has all started so well when Walcott's early strike settled any nerves.
Marouane Chamakh won the ball just inside the Udinese half, with Bacary Sagna playing a clever chip over the defence for Aaron Ramsey to run onto down the right.
The Wales skipper looked up, before clipping the ball across goal, where Walcott arrived at the near post to sidefoot past Samir Handanovic.
It should have been 2-0 soon after, but Thomas Vermaelen, skipper for the night with Robin van Persie suspended, and Gervinho - set to serve a three-match domestic ban for his red card at Newcastle - got in each other's way at the far post following a corner.
Walcott, in the headlines for revelations about England duty from his new book, was booked for a foul on Piccoli Neuton.
It was almost a costly lapse in concentration as Udinese captain di Natale curled in the free-kick from 30 yards, which looped off the crossbar.
Arsenal were let off again on 25 minutes when Alex Song lost possession on the edge of the Udinese box after a corner, and Pablo Armero sprinted clear on into the Arsenal area.
Wojciech Szczesny, though, stood up to make a fine save, with Song then having tracked back to block Mauricio Isla's follow-up effort.
Udinese continued to look the more lively as half-time approached, with di Natale shaving the outside of the post after making space for himself in the six yard box.
Arsenal were forced into a change at the restart, with Johan Djourou replacing England defender Kieran Gibbs, reported to have a tight hamstring, and Vermaelen switching to left-back.
The Swiss international was soon in the thick of the action, sliding in to block di Natale's close-range effort.
However, Djourou did not last long, as he limped off after 54 minutes to be replaced by Carl Jenkinson, the youngster making his debut following a summer move from Charlton.
Jenkinson - who was playing non-League football on loan at Eastbourne Borough last season - was outmuscled by Isla, as the Chilean charged into the right side of the Arsenal area, but could only fire across goal.
Udinese sensed Arsenal were there for the taking, as Armero fired an angled drive over from 20 yards.
Walcott spurned a great chance to ease the pressure when he latched onto a defense-splitting pass from Ramsey, but the England forward mishit his first-time chip, which bobbled horribly wide.
Wenger - who had been sending messages to the dugout via assistant Boro Primorac - made a final change when Tomas Rosicky was replaced by defensive midfielder Emmanuel Frimpong.
With 15 minutes left, Szczesny made a flying save to beat away a curling 25-yard free-kick from di Natale as again Arsenal were forced onto the back foot.
Walcott almost made it 2-0 in stoppage time, but was denied by a fantastic reaction save from Handanovic as Arsenal had to be content with just the slenderest of margins to defend in Italy next week.