Alan Archibald, the Partick Thistle manager, insisted it was a case of job done after his side stepped over this Scottish Cup banana skin.
Irish striker Conor Sammon struck either side of Ross Fergusson’s effort to send the Premiership side into the fifth round.
However, it was a hard-fought afternoon for the Jags at Palmerston and Archibald admitted: “There is always relief. It’s never easy.
“We say there’s usually a shock in every round of the cup, whether it’s the FA Cup or Scottish Cup. We said to not let it be us and we’re delighted it’s not us.”
Partick were making a tricky tie even more difficult with mistakes at the back almost letting the Doonhamers in twice.
A back-pass from Abdul Osman was seized upon by Fergusson but Jags keeper Tomas Cerny was off his line quickly to smother.
Lessons were not learned, however, with Adam Barton’s header to his keeper short and Fergusson again nipped in only to chip inches wide and Stephen Dobbie tested Cerny with a fierce drive before Partick took the lead in the 42nd minute.
Queens were architects of their own downfall after failing to clear from the edge of the box before Sammon showed great strength and composure to create an opening and fire into the net.
However, the Dumfries side levelled the tie in the 55th minute.
Myles Beerman sent Fergusson clear down the left and the young striker shrugged off Niall Keown to rifle home from a tight angle.
But Thistle clinched their place in today’s draw late-on when Sammon’s shot-on-the-turn in the box wrong-footed Alan Martin and nestled in the back of the net.