The French striker - who looked his usual dangerous self for the 59 minutes he was on the pitch at Broadhall Way - opened the scoring after just 14 minutes with a well-taken left-foot effort after good work from Trevor Sinclair.
However, the 14th minute mark in the second half didn't prove so fortunate for Fredi. Chasing a long ball down the right-hand side, he pulled up sharply clutching his right hamstring - an area that he ironically had problems with early last season - and was forced to hobble off the field to be replaced by young striker Jermain Defoe.
While it wasn't immediately known how serious the damage is, any kind of hamstring strain is normally bad news and Glenn Roeder will now be simply hoping that the 24-year-old striker can regain his fitness in time for the big opener at Liverpool on August 18.
For he was again the leading example of the difference in class between the Hammers and their lower league opponents - proving virtually untouchable for the Conference defenders.
After netting the first, Fredi had a hand in the Hammers' second goal on 17 minutes, as he was fouled in the area by a Stevenage defender, allowing Paolo Di Canio to stroke home his first goal of the pre-season campaign from the penalty spot.
The third goal arrived just four minutes later, as Sinclair's low cross was handled by a defender to signal penalty number two. This time, however, the Italian offered Sinclair the chance to get on the scoresheet, and he repaid the favour by slamming home from the spot.
If the crowd of approximately 5,000 were expecting a goal glut though, they were sadly mistaken, as the visitors took their foot off the gas a little and concentrated on brushing up on their possession skills.
Roeder changed from his regular 4-4-2 formation to a 5-3-2 at the break, pushing Raggy Soma and Sebastien Schemmel out wider as wing-backs and introducing Rigobert Song for his first taste of pre-season action alongside Christian Dailly and Hayden Foxe in the centre of defence.
Chances were few and far between throughout a quiet second 45 minutes, although Roeder will be happy with the fact that his side have yet to concede a goal in their three friendly matches so far, with new keeper David James once again looking in command.
However, that was of no consolation to the manager as he looked back at the most serious legacy of this energetic work-out - the possible loss of his star striker through injury with the Premiership campaign almost upon us.
Said Glenn afterwards: "It's too early to say what the extent of the damage is to Fredi, he will have a scan first thing in the morning and we will go from there.
"Hopefully it will be no more than a few strained fibres and he will be back in 10-14 days but we just can't tell at the moment.
"Obviously it is something that I could well do without - he is a vital part of the team and it would be a major blow if we lost him for a long period."
West Ham: James, Schemmel, Soma, Mehmet, Dailly, Foxe, Sinclair, Carrick (Moncur 66, McCann 87), Kanoute (Defoe 60), Di Canio, Courtois (Song 45).
Click here for video footage of West Ham's victory at Stevenage.