Staines' main claim to fame is being home to Ali G and his Massive. But now they are in da hat for the second round for only the second time in the club's history.
Ali Chaaban saw the Blue Square South side through with a superb individual effort on 21 minutes.
It was his fourth goal in three starts and the 27-year-old of Lebanese descent is making up for lost time.
He explained: "I have been plagued by a knee injury for two years and this was only my third start of the season."
The injury prevented Chaaban from having a trial with Gillingham and he showed what they missed out on.
Chaaban, who still harbours ambitions of making it in the Football League, wants a home draw against non-league opposition next.
He added: "That would give us a good chance of making round three and playing one of the big boys.
"Chelsea would be my choice - for no other reason than the fact that I live there!"
But Staines skipper Danny Gordon fancies a clash with League One high-flyers Leeds - and another face-off with Jermaine Beckford.
He said: "I have had some good tussles with him when he was in non-league and it would be good to have another one - although he has improved immeasurably since then.
"But we have a pretty good striker of our own in Ali C.
"He's a fantastic asset to the club and he's capable of scoring that sort of goal week-in, week-out."
Chaaban's strike saw him skip past two Shrews defenders before guiding the ball across Chris Neal and into the far corner of his goal.
It ended a four-man move that had begun with Harry Hooman's misplaced pass, which Paul Murray showed little appetite to make good.
That typified a display from the League Two promotion hopefuls that had boss Paul Simpson fuming.
Shrews also lost in the first round last year, away at Blyth Spartans.
But this time they crashed out in their own backyard to a side two tiers below them in the football pyramid.
Simpson raged: "We got what we deserved. No disrespect to Staines but we should not be losing games like this.
"The players showed a lack of respect for the competition, the club, the supporters and the shirt.
"I cannot believe that, after last season's embarrassment, it's happened again.
"I thought the players would have learned from the mistakes they made then but they didn't.
"We had three strikers on at the end but barely tested their goalkeeper.
"Our qualities in the box were a disgrace and we made it very comfortable for him."
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