The Foxes had Academy boss Jon Rudkin and coach Mike Stowell in charge following Sven-Goran Eriksson's departure earlier this week.
But there was to be no respite for City under the makeshift management duo as Baldock's double, either side of Julien Faubert's rare strike, secured victory for the Hammers.
The hosts were hanging on at the end, though, after Andy King's two goals kept Leicester in the game and only the woodwork denied them a point late on.
Nevertheless, Sam Allardyce's second-placed side have now won three of their last four outings to keep the pressure on leaders Southampton.
They bossed the opening stages and made the breakthrough after 20 minutes when Mark Noble surged forward unchallenged to the edge of the area before playing in John Carew.
The big Norwegian striker chipped the ball across goal from the byline and Baldock outjumped Lee Peltier at the far post.
And Leicester had barely kicked off when they found themselves two goals behind, Faubert collecting the ball from Joey O'Brien 20 yards out and thumping his first goal since February 2010 past Kasper Schmeichel.
It could have been three five minutes later when Baldock took aim from the edge of the box but his deft curler came back off the crossbar.
Leicester finally woke up towards the end of the first half, and
Robert Green, back in the West Ham goal after a knee operation, pulled off a fine point-blank save to deny Jermaine Beckford.
After the break substitute Freddie Piquionne should have added a third after a mazy run into the area but the Frenchman dawdled on the ball and his shot was eventually blocked.
Instead Leicester pulled one back on the hour when former Hammer Paul Konchesky crossed from the left and King nodded the ball back past Green.
West Ham almost hit straight back but Schmeichel pulled off a stunning save to deny Baldock from six yards out.
Leicester claimed they should have had a penalty when King theatrically tumbled in the area but referee James Linington was not fooled.
And their chances looked bleak with 15 minutes left as Baldock ran through on goal and coolly beat Schmeichel for his fourth goal for the Hammers.
But King smashed a fine 20-yard effort into the top corner to set up a tense finish, and they came agonisingly close to snatching a point but James Tomkins deflected Steve Howard's header onto the crossbar.
