After being reduced to 36/2 in 10 overs, Sibanda (61 from 57 balls) and Taibu (53 from 74 balls) stitched a crucial 110-run partnership from 117 balls for the third wicket to take the Zimbabwe innings forward.
Ervine struck a breezy 66 from 54 balls with nine fours and a six while skipper Elton Chigumbura extended fine support with a quick-fire 38 from 41 balls (3x4, 2x6) for their second and most entertaining century partnership.
The duo stood in a 105-run fifth wicket partnership that came from 86 balls.
Prosper Utseya (19 not out from six balls, 3x4, 1x6) and Greg Lamb (17 from 10 balls, 1x4, 1x6) decimated the Kenyan attack towards the end with 20 runs from the last over to help Zimbabwe post their highest score in the ongoing World Cup.
Zimbabwe took the batting power-play in the 42nd over and scored 50 runs losing just one wicket -- Chigumbura -- while the big-hitting by Utseya and Lamb meant they scored 57 runs from the last five overs.
Kenyans struggled with ground fielding and the work behind the stumps was equally sloppy with the team opting to for batsman David Obuya as wicketkeeper in place of Morris Ouma.
Obuya had to hand over the gloves to Rakep Patel in the 35th over after injuring himself while trying to collect a wide delivery.
Zimbabwe openers Brendan Taylor (26 from 36 balls, 5x4) and Regis Chakabva (9 from 22 balls, 1x4) gave a cautious start to the innings after skipper Chigumbura elected to bat on winning the toss.
After the duo was dismissed, Sibanda played an edgy innings but his knock with seven fours and a six put Zimbabwe back on track, while former skipper Taibu gave fine support with a clinical half-century that helped him cross the 3,000-run mark in one-day Internationals.
Sibanda stepped out to hit Tikolo for a huge six over long-on to notch his 13th ODI half-century but he soon ran himself out in a mix-up with Taibu.
After Sibanda`s dismissal, Taibu, on 45, benefitted from the Decision Review System as Asoka de Silva had to reverse his LBW decision. The former Zimbabwe skipper raced to his 18th ODI half-century after with a boundary off Elijah Otieno in the point region.
But Taibu`s second referral soon after completing his half-century turned out to be futile as the Zimbabwe glovesman`s fine innings laced with seven boundaries came to an end.
The Kenyans struggled badly with their substitute wicketkeeper Patel who missed as many as two clear stumping chances as Chigumbura and Ervine made merry.
Patel missed an easy stumping chance off off-spinner Ngoche when Ervine was on 15. The substitute wicketkeeper fluffed once more, this time from Tikolo`s off-spin when Chigumbura was on 17.
Obuya returned to keep wickets in the 42nd over but the damage had already been done.
In his last International match, Tikolo, who led the side in place of an injured Jimmy Kamande, was the most expensive bowler conceding 49 runs from his seven overs of off-spin.
Earlier, Kenya made two changes to the side bringing in Tikolo and medium pacer Peter Ongondo in place of Kamande and Ouma.
Zimbabwe made one change, bringing in fit pacer Chris Mpofu in place of Shingirai Masakadza.