And the Irish, inspired by the excellent Damien Duff, should have made their second-half superiority count.
Only the woodwork and some desperate defending prevented Ireland from scoring the winner which their unrelenting pressure merited.
Despite Ireland's World Cup campaign being overshadowed by Roy Keane's exit, they matched their opponents in the opening stages.
Chances were scarce, with Ireland's other notable Keane, Robbie, heading wide from Kevin Kilbane's cross.
Shay Given made a superb save to deny Eto'o, who had been put clean through after exquisite interplay with Mboma.
But as the first half wore on, Cameroon started to exert greater control, and with their greater possession came the opener.
A well-worked three-man move saw Geremi release the dangerous Eto'o.
The Cameroon striker danced into the area, nutmegged Steve Staunton and crossed for Mboma to strike home from close range.
Yet Ireland almost equalised on the cusp of half-time.
Ian Harte's powerful free-kick was nearly diverted by Rigobert Song into his own net, but Boukar Alioum was alert to the danger and saved well.
Ireland came out in the second half all guns blazing.
And when Geremi failed to extend Cameroon's lead in the 51st minute, blazing his shot wide, Ireland grabbed their chance.
A poor clearance by Cameroon defender Raymond Kalla fell kindly to Holland, who struck a powerful, accurate shot past the outstretched Alioum.
Robbie Keane almost grabbed the winner for Ireland in the closing stages but his shot rebounded off the post and out of harm's way.
And substitute Steve Reid powered in a thunderous
drive which Alioum just tipped over the crossbar on 89 minutes.
However, Ireland have made an excellent start to their World Cup campaign and, with this result, are well-placed to progress from Group E.
Rep of Ireland: Given, Gary Kelly, Breen, Staunton,
Harte (Reid 78), McAteer (Finnan 45), Holland, Kilbane,
Kinsella, Duff, Robbie Keane.
Subs Not Used: Carsley, Connolly, Cunningham, Dunne,
Alan Kelly, Kiely, Morrison, O'Brien, Quinn.
Booked: McAteer, Finnan, Reid.
Goal: Holland 52.
Cameroon: Alioum, Kalla, Wome, Song, Lauren, Geremi, Eto'o,
Foe, Olembe, Tchato, Mboma (Suffo 69).
Subs Not Used: Alnoudji, Djemba-Djemba, Epalle, Job, Kameni,
Kome, Mettomo, N'Diefi, Ndo, Njanka, Songo'o.
Goal: Mboma 39.
Ref: T Kamikawa (Japan).