We created a hatful of chances with goalkeeper Paul Smith the main reason why we drew a blank, saving from Mido in the first minute and them from Fredi Kanoute three minutes from time.
In-between, he denied Jermain Defoe three times and Michael Brown as Southampton, who also threw bodies into blocks all afternoon, hung on for a much-needed win.
Not that it was one-way traffic by any means. Saints also created and wasted numerous chances, especially in the first half, before Quashie's header after 50 minutes.
Peter Crouch forced Paul Robinson into the save of the match two minutes later but Saints dropped deeper and deeper after that and we just couldn't find the equaliser.
Martin Jol made three changes to the side that beat Forest with Ledley King back for Noe Pamarot and all change up front again, Mido and Defoe in for Kanoute and Robbie Keane.
The action started as early as the first minute when Brown hounded Redknapp off the ball, it ran to Mido in the box and he had time to compose himself but Smith saved his low strike with his right foot.
Camara soon shot over at the other end and Brown failed to connect with Carrick's corner as play swung from end to end.
King was at his best to block from Camara and Crouch and then our best chance of the half, Robinson's long kick found its way to Defoe and as Higginbotham stumbled, he had time to pick his spot - Smith deflected it over.
We had a couple of chances from our right as Kelly was found by Davies in space and Mido burst past Le Saux and Bernard only for the final ball to let us down on both occasions.
In-between, Le Saux clipped a fine ball over the top to Camara and with no offside flag, the striker was through. Robinson started to come out, stopped but was big enough to parry as Camara attempted a lob.
Southampton still had two further chances and a penalty appeal waved away in the final eight minutes. Camara missed his shot from six yards after Crouch nodded back Redknapp's corner, Le Saux fell under Kelly's challenge, no penalty and then arguably the chance of the half, Crouch failing to hit the target from six yards from Camara's cutback.
The second half picked up where the first left off. We started on top as Smith saved well from Brown and Mido bobbled a shot wide but then Southampton grabbed what turned out to be the vital goal.
It stemmed from a substitution as Mikael Nilsson came on for Rory Delap and within seconds, whipped in a superb cross that Quashie only had to meet to score, he did just that about 10 yards out.
Still the chances came. Within a minute of the goal Defoe tested Smith at his near post, play went straight up the other end as Robinson somehow kept out Crouch's point-blank header and then Defoe found himself facing Smith again - the keeper coming out on top again with a save to his right.
Southampton started to sit deeper and deeper and were barely a threat in the final half-hour. Play became bitty, interrupted by substitutions and it took until three minutes from time for the final chance - no surprises as Smith came up big again for Saints after Reto Ziegler's excellent through ball sent Kanoute through on goal.
GUIDE TO THE ACTION
1min: SAVE. Brown won possession from Redknapp, ball ran to Mido in box, chance to compose himself, Smith saved with right foot.
5mins: Reid into Mido, chested down to Defoe who hit 22-yard volley straight at Smith.
7mins: Telfer won 50-50 with Edman, Camara onto loose ball, into box and shot over under pressure from King.
10mins: Brown's 20-yarder looked on target until blocked by Higginbotham.
14mins: CHANCE. Brown failed to connect with free header from Carrick's inswinging corner.
15mins: CLOSE/CHANCE/BLOCK. Camara got better of Kelly in box, Crouch inches away from cross but Telfer kept ball alive, picked out Quashie, he got volley all wrong but fell to Camara, 10 yards out, King there to make superb block.
19mins: CHANCE. Crouch got better of Kelly this time from huge Smith clearance, tight angle, opted to shoot, King there again to block.
25mins: SAVE. Robinson long clearance found its way through to Defoe as Higginbotham stumbled, completely free in box, Smith managed to deflect over bar.
29mins: Best move so far ended with Davies playing Kelly into box, not the best first touch and blazed shot over.
32mins: SAVE. Le Saux clipped ball over top to Camara, no offside flag, Robinson started to come off line and stopped but Camara didn't get enough on lob and Robinson able to tip ball into air and collect it.
35mins: CHANCE. Mido burst his way through Le Saux and Bernard, to byline, had Defoe and Reid in close support but cross-come-shot evaded everyone.
37mins: MISS. Redknapp's deep corner nodded back by Crouch to Camara, six yards out, completely missed kick.
41mins: PENALTY? Le Saux went down under Kelly's challenge but appeals waved away.
45mins: MISS. Camara managed to shrug off Gardner, got to byline, pulled back to Crouch who missed target from six yards.
Half-time: Southampton 0, Spurs 0
46mins: SAVE. Brown into box, cut back onto right foot, low curler saved well to his left by Smith.
49mins: CLOSE. Ball bouncing around in area, King half-shot fell to Mido who bobbled shot just wide from 16 yards.
50mins: SUB. Nilsson for Delap.
50mins: GOAL. Nilsson's first touch provided goal, whipped in cross from right that Quashie headed home from 10 yards.
Southampton 1, Spurs 0
51mins: SAVE. Straight up the other end and Defoe worked a yard in box and cracked shot at near post that Smith palmed wide.
52mins: SAVE. Save of match, Crouch met Redknapp's free-kick just six yards out, downward header somehow parried into air by Robinson, Mido there to complete clearance.
55mins: SAVE. Defoe led Lundekvam and Bernard a merry dance cutting in from left but Smith there again to deflect into side-netting.
57mins: SUB. Kanoute for Mido.
60mins: Deep cross from Kanoute missed by Telfer, Reid managed to hook over stranded Smith but ball wouldn't come down for Defoe.
62mins: Defoe cut in from left again, let fly but shot hit Lundekvam.
68mins: SUB. Ziegler for Kelly.
71mins: YELLOW. Edman for foul on Nilsson.
75mins: SUB. Keane for Reid.
79mins: Camara latched onto Lundekvam's clearance but sliced shot wide.
85mins: YELLOW. Quashie for foul on Ziegler.
87mins: SAVE. Magnificent pass from Ziegler released Kanoute, clear on goal, Smith out to block with legs.
88mins: SUB. Svensson for Le Saux.
Injury time: YELLOW. Brown for dissent.
Full-time: Southampton 1, Spurs 0
Southampton: Smith, Delap (Nilsson, 50), Lundekvam, Higginbotham, Bernard, Telfer, Redknapp, Quashie, Le Saux (Svensson, 88), Camara, Crouch. Subs: Phillips, Cranie, Blayney.
Spurs (4-4-2): Robinson; Kelly (Ziegler, 68), King, Gardner, Edman; Davies, Carrick, Brown, Reid (Keane, 75); Mido (Kanoute, 57) , Defoe. Subs: Cerny, Keane, Pamarot.
Nigel Quashie's header won it for Saints as we left St Mary's wondering how we failed to score in Saturday's Barclays Premiership clash.