Those goals silenced any hint of controversy after referee Mike Riley disallowed an opportunist Thierry Henry strike three minutes before the interval. Only Oakes stood between Wolves and a rout as Vieira-inspired Arsenal relentlessly stepped up the pace in the second half.
A generation ago, an Arsenal v Wolves FA Cup fourth round tie would have been eagerly awaited throughout the land. Now the most important question was, how much of a weakened team would Arsenal field? The Champions League and the Premiership have taken priority over the FA Cup by some distance.
Yet, even while Wenger has rested senior players, Arsenal have reached the FA Cup semi-finals in six of the last seven seasons. The Gunners have now beaten Wolves six times in six matches under Wenger, including the 1998 FA Cup semi-final.
Wenger fielded an experimental defence, in which Sol Campbell was the only regular. Arsenal were without the suspended Kolo Toure so Pascal Cygan stood in while Jens Lehmann was restored for a rare appearance in goal.
Wenger wanted his strikers to play themselves back into scoring form. Henry had not scored for five matches while Jose Antonio Reyes had scored twice in 19. This was a frustrating afternoon for both of them, Henry most of all.
In midfield, it was just like old times as Vieira and Wolves veteran Paul Ince fought to establish midfield supremacy. Ince was booked for a challenge on the Arsenal skipper.
Ince said that Wolves would have to defend with resolution and grab any half-chances if they were to spring a shock. They defended with determination but could not respond to South Korean attacker Ki-Hyeon Seol's prompting.
Glenn Hoddle has changed Wolves' tactics from 4-4-2 to a midfield diamond. Seol played furthest forward and broke to support lone striker Carl Cort. He gave Arsenal an early warning with a 20-yard shot that tested Lehmann.
Henry soon probed Wolves' back line, nipping past their offside appeals to collect Cygan's pass, before overhitting his cross for Robin van Persie. Reyes cutting in from the left then fired an eighth-minute effort wide.
Wolves were restricted to shooting from distance. Lee Naylor drove wide from 30 yards, then Lehmann held Mark Kennedy's attempt.
Oakes rescued Wolves in the 21st minute, tipping away Van Persie's drive after the Dutchman skipped past two tackles.
Arsenal right-back Emmanuel Eboue, combining with Ljungberg, then burst into the box and hit a shot that smacked off the bar. Reyes had a volley deflected wide by Joachim Bjorklund, then struck a 30th-minute drive past an upright. He shot over again after a break by Ljungberg.
In between, Seol - finding space on the left - gave Arsenal another scare with a dangerous cross and Seyi George Olofinjana failed to test Lehmann with his header.
Henry thought he had broken the deadlock in the 42nd minute. Oakes threw the ball up to kick out. Henry flicked it away from him and tucked it into the net but Riley ruled it out for a foul on the keeper. The decision clearly upset Henry who spent the rest of the game in argumentative mood.
Henry's colleagues seemed to let their minds wander too a minute later, as Carl Cort met Shaun Newton's cross with a header that forced Lehmann to a flying save.
Seol continued to offer Wolves' biggest threat and Cort met his 47th-minute cross with a header that fell just behind Olofinjana.
By now though, Vieira was driving Arsenal forward. Oakes beat out his 51st-minute header and a minute later Vieira's pass picked out Reyes who was blocked by Bjorklund.
Henry pounced on the loose ball and went down under Oakes' advance and Vieira calmly tucked away the penalty. Wenger thought Riley could have given a spot kick for either challenge.
The Wolves keeper kept his side in contention with brilliant saves from Van Persie's volley, Ljungberg's drive and a Henry shot.
Hoddle sent on striker Kenny Miller for defender Bjorklund as Wolves tried to chase the game but Vieira's energy ensured that the momentum stayed with Arsenal.
Oakes pulled off another excellent save to thwart Henry's low shot as he burst onto Van Persie's pass and the keeper then saved Ljungberg's strike with his feet.
Ljungberg finally ended Wolves' resistance eight minutes from time. Henry met Robert Pires' cross with a deft flick and the Swede volleyed into the roof of the net.
The return of Lescott, sidelined by injury last season, has strengthened Wolves' defence.
Yet, even with stars rested, Arsenal emphasised the gap between the top of the Premiership and Championship play-off hopefuls.
Now Wolves can concentrate on climbing towards those play-offs, while Arsenal chase their tenth FA Cup triumph.
MAN OF THE MATCH: Michael Oakes (Wolves) - He made a series of brilliant stops that saved his side from a rout.