Yakubu's second-half brace moved Portsmouth out of the bottom three but extended Manchester City's winless run.
Dejan Stefanovic headed Pompey in front from Patrik Berger's right-wing free-kick but Nicolas Anelka volleyed City level from Trevor Sinclair's nod down.
City hit the bar three times before Sibierski made it 2-1 from 14 yards.
But Yakubu drilled home from the edge of the box and latched on to Arjan De Zeeuw's long ball to score either side of a Teddy Sheringham header.
Eyal Berkovic made his debut for struggling Portsmouth following his midweek £500,000 move from City.
Kevin Keegan opted to leave Steve McMananman, who has been hampered by a hamstring problem, on the bench and start with Frenchman Sibierski.
The home team opened brightly and Alexei Smertin wasted their first opportunity, firing over from 16 yards, while Ayegbini failed to take advantage of a defensive mix-up between Richard Dunne and keeper David Seaman.
The former England goalkeeper was then forced off the field after injuring his left shoulder in a challenge with Ayegbini.
His replacement, Kevin Stuhr-Ellegaard, was beaten seven minutes after coming on, when Stefanovic leapt unchallenged to head home Berger's free-kick after Joey Barton fouled Berkovic.
But City hit back with a well-worked goal by Anelka.
Fowler crossed to Sinclair and his header back across the box was diverted into the roof of the net by Anelka with a measured volley.
19 mins: Stefanovic scores
21 mins: Anelka equalises for City
45 mins: Sibierski fires City ahead
52 mins: Yakubu levels for Portsmouth
58 mins: Sheringham extends lead
77 mins: Yakubu wraps up victory
The pace lifted and Fowler slammed a 20-yard drive onto the bar for the visitors before Yakubu hit a stinging drive straight at Ellegard and Smertin dragged the rebound wide.
Fowler nodded onto the top of the bar, and Sibierski curled a 20-yard free-kick onto the bar as City hit the woodwork for the third time in six minutes.
But the midfielder finally fired Kevin Keegan's side ahead after Anelka nodded on to end a pulsating opening half.
Yakubu started the second half in spectacular fashion, latching on to a pass from Sheringham, who had expertly evaded Richard Dunne, to slot Pompey level.
Barton thought he had levelled again for City a minute later, but his thunderbolt was ruled out as Anelka was in an offside position.
Sheringham headed home Berger's free-kick after Yakubu had been fouled to make it 3-2.
And Yakubu wrapped up the victory after collecting De Zeeuw's long pass and firing left-footed past Ellegaard to lengthen Manchester's winless streak to 14 games.
Portsmouth: Hislop, Primus, Stefanovic, Pasanen, De Zeeuw,
Hughes, Berkovic (Harper 74), Smertin, Berger, Sheringham,
Subs Not Used: Wapenaar, Taylor, Schemmel, Roberts.
Man City: Seaman (Stuhr-Ellegaard 13), Sommeil, Dunne, Distin, Tarnat, Sinclair, Barton, Bosvelt, Sibierski, Fowler, Anelka.
Subs Not Used: Wiekens, Macken, McManaman, Tiatto.
Booked: Dunne, Fowler.
Referee: M Messias (N Yorkshire).