Kenny Jackett's men eased to a comfortable 4-0 win in this afternoon's FA Cup encounter.
Yet it wouldn't be until the 43rd minute before the Blues made their breakthrough at York Road.
Thompson converted Ronan Curtis' left-wing cross to hand the visitors the lead '“Â with Oli Hawkins, Jamal Lowe and David Wheeler netting in the second half.
Yet before Thompson struck, Ayo Obileye provided a scare when he smashed a shot against Craig MacGillivray's left-hand post.
And it's Jackett's men who now await their opposition in Monday's second-round day.
Thompson said: '˜The first half was a bit shaky at times, they got into the game and we were on the back foot a little bit at times during spells.
'˜To put the side ahead with the first goal was a great feeling and we kicked on from there.
'˜The second half was a bit easier for us '“ and we came here and did the job.
'˜Maidenhead caused us some problems, we caused them some problems and it was quite a close encounter in the first half, we were patient and got the result we needed.
'˜They hit the post, they came close, who knows if that goes in it could have changed the game.
'˜But at the end of the day we got the win and are through to the next round and that's all that matters '“ that's what we came here for.'