Striker Baldock volleyed home his fifth goal for the Hammers since arriving from MK Dons in August in the 49th minute and Collison applied a cool finish eight minutes later after the visitors had withstood a first-half bombardment at the KC Stadium.
Hammered: Hull's Liam Rosenior ducks into the challenge of Sam Baldock (right)
MATCH FACTSHull: Gulacsi, Rosenior, Chester, Hobbs, Dudgeon, Evans, McKenna, Koren, Fryatt, Adebola, Mclean. Subs not used: Basso, Cairney, McShane, Harper, Brady.
West Ham: Green, Faubert, Tomkins, Faye, McCartney, Noble, Collison, Nolan, Diop, Baldock, Carew. Subs not used: Kurucz, Cole, Sears, Potts, Piquionne.
Referee: Nigel Miller.
Hull completely dominated the first 45 minutes, but squandered several chances, while former England goalkeeper Robert Green was in fine form for the Londoners.
Green pulled off fine saves to deny Robert Koren and Matty Fryatt in the first half and turned away Aaron Mclean's goalbound effort in the second, but Sam Allardyce's side refused to yield and clinically despatched their chances to maintain their impressive away form this season.
Dele Adebola made his first start since the opening day of the season for Hull, up front alongside Fryatt,and Peter Gulacsi replaced injured goalkeeper Adriano Basso who was outwith a knee injury.
Defender Abdoulaye Faye, striker John Carew and midfielders Papa Bouba Diop and Collison all returned forWest Ham following their goalless midweek draw with Bristol City.
Green was by far the busier of the two goalkeepers in the opening exchanges.
Towering presence: James Chester (right) is held off by John Carew
The former England number one turned away Koren's angled drive at full stretch in the fourth minute and twicedenied Fryatt, holding his shot from inside the penalty area and then the striker's header from Liam Rosenior's cross.
Hull made all the early running and Green was at his best again in the 28th minute when keeping out another long-range effort from Slovenia international Koren.
West Ham's travelling fans had to wait until the 31st minute before their side's first effort on goal, defender James Tomkins heading Kevin Nolan's corner wide.
Nolan then headed off target himself soon after following Julian Faubert's cross, but Hull finished the firsthalf on top and only a timely intervention from Faye prevented Adebola's goalbound shot from inside the area giving the home side a 42nd-minute lead.
Green did well to hold another shot from Fryatt and Mclean squandered a gilt-edged chance from 12 yards on the stroke of half-time.
Hammers boss Allardyce withdrew Carew in favour of Carlton Cole at the break and the switch appeared to pay dividends when the visitors snatched the lead.
Bouba Diop's headed pass teed up Baldock inside the area and he lashed home a volley high into the roof of the net from six yards.
Battle of the big men: Dele Adebola (left) challenges Carew
Hull were rocked having dominated the first half, but worse was to follow for Nigel Pearson's side.
Forced to chase the game in search of an equaliser, the Tigers were caught on the counter-attack as West Ham doubled their lead.
Cole's neat pass caught the home defence flat-footed and sent Collison clear on goal and the Hammers midfielder kept his composure to bury the ball into Gulacsi's bottom right-hand corner.
Hull rallied and Hammers defender Faubert blocked Jack Hobbs' angled drive and Green turned away Mclean's left-footed effort from the left side of the area.
Green held another effort from Koren in the 82nd minute and kept out Hobbs' header, while Tigers substitute Robbie Brady dragged a shot wide as Hull slipped to a second successive defeat.
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