Blues boss Paul Sturrock made three changes to his side after the FA Cup replay defeat to Macclesfield.
Former Shrews skipper Graham Coughlan was fit enough to start, as was Bilel Moshni to join him in central defence which was a pleasant surprise, Luke Prosser dropping to the bench after picking up a foot injury last Tuesday.
On the left Louie Soares was preferred to Sofiene Zaaboub while up front Blair Sturrock replaced Barry Corr, Luggy sticking with Oxford loanee Jack Midson.
Ryan Hall sadly stayed in the stands due to the continuing problems with his knee.
As for the great escape for the Shrimpers at their first visit to the Greenhous Meadow; well, with three minutes left on the clock some of the home crowd may have been leaving for the exit as Shrewsbury held on to their 49th minute lead, but Grant's sixth strike of the season grabbed a very welcome late point.
The Shews could have taken the lead as early as the 13th minute when nine-goal Jake Robinson found himself one on one with Glenn Morris and tried to take the ball around the Southend shot stopper, who preceded to grab the ball off the forwards feet, great keeping.
Bar a poor Soares header it was mainly Shrewbury who looked most likely and were trying to uphold an unbeaten record at home that they didn't look like losing here.
And eight minutes after the first Robinson effort he tried again, a low shot that fizzed past the right hand post of the Morris goal.
However, on the half-hour, Grant did make one of his trademark runs into the Shrews penalty area, but this time without the ball, as he waited for a fine right-wing Clohessy cross which he hit volleyed wide of the post, from three yards, with his left foot! Luckily he learnt a lesson from that!
Time then for Robinson to miss another great chance to score after a Morris cock-up, consistancy not Glenn's strong point, which left the Blues keeper a hopeless bystander as the Shrews striker looked odds-on to tap the ball into the back of the net but embarrassingly failed to make contact. Oh dear!
So half time came with the Shrimpers support believing that after those let-offs the game may turn their teams way. Wrong.
Four minutes after the break Robinson turned provider by crossing for, yes, former Southend striker Matt Harrold, who headed the ball neatly back for Mark Wright to say thanks very much and drill the ball past Morris into the left hand corner.
As ever Luggy reacted quickly with a substitution, QPR loanee Antonio German replacing Blair Sturrock up front, which certainly helped make the Shrimpers look more competitive without giving Shrews 6 foot 2 keeper Chris Neal any real problems.
Wright nearly had a brace to celebrate but Morris saved well from his low strike from the edge of the penalty area while in the home penalty area Grant saw his effort gathered by Neal under pressure.
At the other end young Bilel was yellow carded for taking offence to some sliding tackles into his keeper and reacted the way he tends to do, the Shrimpers skipper Craig Easton having to help keep him from adding another red to his collection!
Last cards on the table time for boss Sturrock, strikers Barry Corr and Harry Crawford taking over from Losh Simpson and the uninspiring Midford with only seven minutes remaining.
However, it didn't seem it would be enough until the 87th minute when Captain Craig found Anthony Grant lurking with intent at the back post and the former Chelsea trainees' volley crashed into the top right hand corner from eight yards.......with his left foot!
Uncle Ron must be rubbing his hands with glee at the fee Granty may get for him, sorry the club, come the January sales!
The travelling faithful celebrated, and both team and fans now travel to Stevenage Tuesday evening in much better spirits that may have seemed possible before the game.
Southend player markings: Morris - 7, Gilbert - 6, Moshni - 8, Coughlan - 6, Clohessy - 7, Grant - 6, Easton - 6, Soares - 5, Simpson - 6 (Corr 83), Midson - 4 (Crawford 83), Sturrock -6 (German 55 - 6).
Referee - Mr. R. Shoebridge - 5.