With two minutes remaining at the Riverside Stadium, Shots striker Danny Hylton scored his eighth FA Cup goal in four games to set up a lucrative replay for the npower League Two side, following Lukas Jutkiewicz's late opener.
Hylton still leads the scoring charts but Jutkiewicz ensured he will not add to his tally by sparing Boro a tiring trip to Hampshire with a winner five minutes into stoppage time.
Non-league Luton, who dispatched Premier League outfit Norwich, are now the lowest-ranked team in the pot for the fifth round but Mowbray would gladly welcome Manchester City, Arsenal or other top-flight opposition to Teesside.
He said: "Managers only ever want a home tie and in an ideal world it wouldn't be someone from our league.
"I'd like to play a Premier League side or one of the lower-league teams who've done well today (Saturday).
"The FA Cup starts getting exciting in the fifth round as you're one game away from the quarter-finals.
"Let's see who we get. If we play Manchester United or Arsenal the onus is not on us to break them down, it's on them to break us down and if they get frustrated every time a move breaks down we can counter.
"Either is suitable for us. A top team that we can frustrate or a lower league team we can give problems and try to get through to the next round."