Scott McGleish had a great chance to put the League One club into the lead, but his low strike was turned around the post by Boaz Myhill.
Ibanez – signed from Atletico Madrid in the summer – headed in on 12 minutes for a much-changed Baggies side, with substitute Wood making sure there was no late drama by slotting in a second during stoppage time.
With a trip to Liverpool at the weekend, West Brom boss Roberto di Matteo was taking no chances as the likes of goalkeeper Scott Carson, Scotland midfielder Graham Dorrans and striker Peter Odemwingie, who scored on his debut against Sunderland, were all left on the bench.
Despite the draw of Premier League opposition, there were plenty of spare seats at the Matchroom Stadium – with a couple of non-paying guests taking up the view from the flats which now stand at all four corners of the development.
West Brom created the first opening when Giles Barnes’ low shot was held by Jamie Jones.
However, the tie could have turned out so differently had things gone Orient’s way on eight minutes when the ball broke to McGleish at the edge of the penalty area.
Stand-in Baggies keeper Myhill, though, stuck out a hand to make a fine save at full stretch, turning the ball around the far post.
Slowly, the Baggies started to find more space as Luke Moore cut inside from the left and drilled wide, with impressive youngster Sam Mantom – on his senior debut – then firing an angled drive into the sidenetting.
Only a fine save from Orient keeper Jamie Jones prevented Moore firing the Premier League side ahead on 27 minutes, diving to his right at full stretch.
There was, though, little the Orient number one could do when the Baggies took the lead shortly after.
Mantom whipped a free-kick from the left into the area, where former Spain international Ibanez guided a header into the far corner from 12 yards.
It was almost 2-0 a minute later when Simon Cox smashed a rising shot just over.
Orient enjoyed a decent spell as half-time approached, with Charlie Daniels testing Myhill with a dipping effort from the edge of the penalty area.
There was certainly more urgency about Russell Slade’s men following the restart, with Adam Chambers almost getting on the end of a low cross into the six-yard box from Jimmy Smith.
The League One side sensed a way back into the tie and pushed the Baggies back into their own half.
However, West Brom were not really stretched and seemed happy to play on the break.
Orient broke clear and Chambers chipped the ball into the penalty area, where McGleish arrived at pace. However, the much-travelled veteran could only steer his header wide.
At the other end, West Brom should have gone 2-0 ahead when Wood knocked the ball down for Cox, but he sliced the loose ball wide.
McGleish was picked out by a looping ball to the far post, but his header was caught under the bar by Myhill.
There were half-hearted appeals for a penalty when the ball bobbled up off Ibanez, but referee Dean Whitestone was unimpressed.
On 85 minutes, West Brom had to make another change when Cech picked up an injury and Gonzalo Jara came on.
The Baggies secured safe passage into the third round when New Zealand forward Wood cut in from the right to drill a low shot under Jones in stoppage time.