Despite a positive start, the visitors found themselves three down after a quarter of an hour, with Danny Hoesen breaking clear and opening the scoring, finishing confidently under the dive of Colin Doyle.
Recalled from his loan spell at Bristol Rovers, Wayne Brown then doubled the Whites' lead by cutting inside Luke Rowe on the right of the visitor's box and firing in at the near post.
Two then became three following a break on the counter, with Hoesen eventually winning a corner down the right. Christopher Buchtmann then supplied the delivery, with Matthew Briggs heading home at the back post.
Briggs, another who has spent time out on loan in recent weeks, went close to a fourth moments, later drilling a low shot at Doyle, while Fulham's 'keeper Neil Etheridge denied Kevin Phillips with a smart stop.
Hoesen mistimed an opportunity on the half hour mark, with Freddie Stoor and Okaka linking well on the right, before the latter powered through the City defence, only to be denied by an excellent block from ex Fulham man Franck Queudrue.
With more chances falling for the hosts, Hoesen drew a fine save from the hands of Doyle, while Kagisho Dikgacoi almost found the net with an ambitious overhead-kick.
Birmingham certainly enjoyed their share of possession, but for all their intricate one-twos, the visitors were swept back with Briggs marshalling his defence with composed authority.
As a result Fulham deservedly entered the interval three goals to the good, and manager Billy McKinlay no doubt pleased, with his side organised, confident and forward thinking.
Birmingham started the second-half in spirited fashion, suggesting there could well be a few twists and turns in store for the home side.
Teemu Tainio tried his luck from distance, while James O'Shea skewed a chance wide when well-placed in the right of the Fulham box.
O'Shea's cross for Phillips then flashed across the Whites' goalmouth, before Cheick Toure robbed the veteran striker of a chance with a brilliant last-ditch tackle.
With the final 15 minutes approaching Queudrue tested Etheridge with a fierce low strike, before the Frenchman fired narrowly wide from 20 yards following an intelligent lay-off from Jake Jervis.
Despite the visitors seeing more of the ball, Fulham looked content and with Okaka an outlet on the break the Birmingham defence were continually forced into action.
At the other end, Briggs and co. kept their cool to register a fourth consecutive clean sheet.
Birmingham may have entered the match on the back of three straight victories, but it was the Whites who stretched their unbeaten run - which now stands at seven games.
That impressive form will certainly be tested again next week, with Billy McKinlay's side facing derby rivals Chelsea. A win at Motspur Park next Tuesday March 23rd, Kick-Off 7.05pm, would see Fulham leapfrog the Blues to third in the Barclays Premier Reserve League South table.
Fulham Reserves: Etheridge; Stoor, Marsh-Brown, Briggs, Toure; Dikgacoi (Smith 65), Milsom, Brown, Buchtmann; Okaka, Hoesen (Payne 71). (Subs not used): Bettinelli, Pierre, Harris.
Birmingham Reserves: Doyle; Ozturk (Dunphy 69), Rowe, Kerr, Queudrue; Michel (Sammons 75), Tainio, O'Shea, Shroot; Phillips ( Redmond 75), Jervis. (Subs not used): Butland, Asante .
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