The build-up to the game was typified by struggling teams and under-pressure managers, with Fulham boss Martin Jol coming in for heavy criticism as his side sat in 18th before the game.
West Ham were not faring much better, however, and, in 17th, many home fans were calling for a change of manager at Upton Park.
A convincing victory at home over potential relegation rivals will perhaps take the pressure off Allardyce in the Hammers hotseat, however, as they rise to 15th with the result.
Even after taking the lead through Mohamed Diame's deflected effort however, Allardyce remained on the edge of his seat.
"It was a bit nervous and twitchy going into the last 15 minutes," Allardyce told Sky Sports. "I was getting a little worried that Fulham might get one on the break.
"The lads defended really well from that point of view, and when the subs got on they had more energy and exposed that defence a little more.
"In the end, what we needed most of all was a fantastic result and it was a very good performance."
The aforementioned substitutions certainly settled the game for West Ham, as Joe Cole, Carlton Cole and Ravel Morrison all played a huge part in the decisive last two goals, with both Coles netting late on.
Allardyce was quick to praise a couple of his starters, however, with under-fire striker Maiga and winger Downing coming in for particular praise.
"Maiga had a good game today, proving that he can compete," added Allardyce. "We're just waiting for that goal.
"Stewart Downing is, for me, a different class, and he continues to probe and open defences up.
"The subs paid off in the end, and with the fresh legs we ended up winning comfortably."
Just nine goals from 12 league games have represented West Ham's biggest worry so far this season, and so a three-goal haul will be pleasing for the Hammers.
Allardyce pointed also towards a sixth clean sheet in the league as his side pulled away from the relegation zone with the win.
"It's a clean sheet again. We could have had more goals too, so it's all been there today. Finally we've got the result to go with it.
"It's a relief. Especially when you're a manager in this position, because it's one you have to take on your own shoulders.
"You have to continue to keep the lads in a good frame of mind. Have a laugh with them, and when it gets serious you have to get serious."