The last time that the Hammers had left their opponents firing blanks was at Fulham back in February and, 27 matches on, they had Robert Green to thank for keeping their goal intact in a dour draw that saw ex-Hammer Jermain Defoe force some fine saves, while at the end Craig Bellamy cracked the crossbar.
With a total of just a dozen matches in official charge of their clubs, both bosses had kicked off still wearing their Premier League L-plates.
Gianfranco Zola, who had only recorded two victories during his nine games in the Hammers hot-seat, was able to recall Valon Behrami and Carlton Cole alongside Jack Collison following last weeks collapse against Everton, as Luis Boa Morte stood down together with substitutes Lee Bowyer and Julien Faubert.
After securing victory at the third attempt last Saturday, Adams made two changes from the side that won at Sunderland, as Younes Kaboul and Papa Bouba Diop replaced Niko Kranjcar (ankle) and Sol Campbell (toe).
There were also three former Hammers in the Pompey line-up and, as David James and Glen Johnson looked on, Defoe almost gave his side a tenth-minute lead but he hooked over from six yards as Green bravely dived at his feet.
And after Adams was forced to introduce substitute Armand Traore, once Lassana Diarra had failed to recover from a twisted ankle sustained in a crunching foul on Scott Parker, Johnson unleashed a stinging 20-yarder that the Hammers keeper held at the second attempt.
With Fabio Capello looking on, Peter Crouch also volleyed James Collins' poor clearance wide from 18 yards, before Defoe's low shot was deflected behind by Herita Ilunga.
Without a win over Pompey in a six-match run stretching back to January 1993, West Ham's lethargic first-half performance suggested that it would still be another 15 years before they record a victory over the Fratton Park outfit.
Indeed, although Sylvain Distin went unpunished for handling Freddie Sears' cross before Collison unleashed a couple of efforts and Parker tried his luck from distance, James enjoyed a peaceful 45 minutes upon his return to the East End.
Matthew Etherington replaced the subdued Sears for the restart, but while the Hammers were looking for some elusive pace and purpose, it was Portsmouth who had it in abundance.
Indeed, Defoe soon rode Lucas Neill's tackle before letting fly with a rising 15-yarder that Green palmed skywards and, seconds later, the England striker got the better Collins before seeing his attempted lob gathered by the Hammers keeper.
On 53 minutes, West Ham finally mounted their first serious challenge on the visitors' goal, when Bellamy's 20-yard free-kick crashed back off the crossbar and then Collison saw his low follow-up gathered by the relieved James.
Zola introduced Julien Faubert for the leggy Ilunga and, with the claret and blue fans amongst the 32,328 crowd beginning to stir at long last, West Ham finally juddered out of first gear as Behrami's far-post header was collected by the Pompey keeper.
In reply, Tony Adams opted to replace Crouch with Nwankwo Kanu and the visitors might even have snatched it with five minutes remaining.
But under pressure from a retreating Matthew Upson, the breaking Defoe saw his low, angled shot cannon behind, after Green blocked with his outstretched legs to finally secure that long-awaited clean sheet.