The Hammers looked set to make it a perfect start for onlooking new owners David Sullivan and David Gold after Younes Kaboul's attempted clearance bounced in off Matt Upson in the 52nd minute.
Webber levelled two minutes after coming on to keep alive Pompey's faint hopes of avoiding the drop.
The match sparked into life with five golden opportunities in a sensational three-minute spell midway through the first half.
Goalkeeper Asmir Begovic came to Pompey's rescue with a fine double save to first block Frank Nouble's close-range effort and then palm away Alessandro Diamanti's follow up.
At the other end England World Cup hopeful Robert Green did well to turn Aaron Mokoena's 21st-minute drive behind before Mark Noble cleared Kaboul's swivelling shot off the line from the resulting corner.
Begovic produced another brilliant fingertip save to turn Jack Collison's curling effort wide of his left-hand post.
Bosnia international Begovic was powerless to prevent West Ham taking the lead in fortuitous circumstances seven minutes after half-time.
Pompey failed to properly clear Diamanti's corner and Kaboul's attempted back headed clearance from the Italian's follow-up cross struck Upson and flew into the net.
Defender Marc Wilson should have equalised nine minutes later but could only put a free header over the crossbar from Angelos Basinas' corner.
West Ham had another lucky escape in the 64th minute when Kevin Prince Boateng fired inches wide after racing onto John Utaka's centre.
Begovic denied Julien Faubert with another excellent reaction save as he clawed the Frenchman's cross-cum shot behind for a corner as the Hammers pressed for a match-clinching second.
Webber equalised 14 minutes from time, getting in behind the West Ham defence to latch onto Utaka's throughball before calmly slotting between the legs of the onrushing Green.