He reacted quickly after home keeper Boaz Myhill had palmed out Denilson's swerving shot.
Hull looked nervous and Jobi McAnuff's deflected shot had keeper Boaz Myhill scrambling across his goal.
The Bolton striker first forced a corner with a 25-yard shot which Boaz Myhill parried.
William Gallas clattered the crossbar in the 83rd minute before a brilliant late Boaz Myhill save denied Fabregas.
Half-time substitute Roger Guerreiro brilliantly chipped Wales goalkeeper Boaz Myhill 10 minutes from time to secure victory for the Poles.
Toshack is without a host of players including Premier League quintet Craig Bellamy, James Collins, Jack Collison, Simon Davies and Boaz Myhill.
Spurs responded with spirit, and Roman Pavlyuchenko should have equalised after a mistake by Paul McShane, but could only shoot straight at Boaz Myhill.
Fernando Torres had a 10-yard angled sidefoot tipped over by keeper Boaz Myhill but having survived that early scare Hull quickly set about their task.
Torres dribbled around Boaz Myhill to restore the Reds' lead and rolled in to complete his treble after latching on to a clever Yossi Benayoun pass.
Toshack also pointed out that Hennessey's place could be under increasing pressure from Hull's Boaz Myhill who is likely to playing regularly in the top flight with his newly-promoted club.
The Hammers almost equalised when Cole's shot from five yards out beat Boaz Myhill, but he saw his effort come back off the underside of the bar.
Viduka nearly doubled the lead soon after, skipping past two defenders and cutting in from the right only to drag his shot wide of Boaz Myhill's right-hand post.
Head coach Roberto di Matteo has decided to drop goalkeeper Scott Carson for the Blackpool game, with deputy Boaz Myhill making his first Premier League appearance of the season.
But - apart from Milner's injury-time drive, which was well saved by Boaz Myhill - City created little and West Brom deserved to take their place in the last 16.
Boaz Myhill had to make a great stop to keep out Mohamed Diame's fierce 25-yard strike, then dived at Jason Scotland's feet as he looked to tuck away the rebound.
West Brom's early dominance was almost rewarded when Olsson headed against the bar after Valero's shot was well saved by Boaz Myhill, and Roman Bednar almost squeezed in the second rebound.
Birmingham started the brighter but Doncaster had the game's first chance when James Coppinger fired straight at Boaz Myhill and Simon Gillett then dragged a shot wide after a mix-up in the Birmingham penalty area.
City could have been further ahead at the break, and would have been but for Baggies keeper Boaz Myhill tipping a Kolarov thunderbolt on to the bar and also denying Silva when he was clean through.
Hull repelled the first effort from Matt Taylor but the ball found its way to Steinsson and he drove in a low shot which Tigers keeper Boaz Myhill could only help on its way into the net.
Liechtenstein - who were earlier doomed to a certain bottom-place finish in the group when Azerbaijan drew 1-1 with Russia - showed they had teeth, though, Hasler easily turning new Wales captain James Collins and forcing Boaz Myhill into a save.
For the home side, Harte curled a free-kick narrowly wide, and after Jobi McAnuff created space on the left, Hunt sent in a powerful header from 10 yards that was brilliantly saved by Boaz Myhill, recalled in place of Scott Carson.
At 3-0, West Ham looked down-and-out but the Hammers showed glimpses of the brilliant comeback that was to follow, when Ba found space from Noble's corner only to see his shot expertly palmed onto the post by Boaz Myhill and eventually hacked off the line by James Morrison.
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