Bjarne Pedersen produced the last-heat win which ensured Eastbourne did not suffer a home slip-up.
Pedersen raced away to win heat 15 and ensure full points in the 50-40 success over play-off rivals Lakeside.
Hammers would have taken one of the three points had they managed a 5-1 in heat 15 but Pedersen, who has been struggling with a back injury, comfortably raced clear of Lewis Bridger and Craig Cook.
Eagles were 10-2 up after two races but Hammers made it tough from then on.
Six of the last eight heats finished in 3-3s but a 4-2 led by Pedersen ahead of the previously unbeaten Cook in heat ten restored the eight-point lead.
Kyle Newman, impressive as guest reserve, fended off Richard Lawson in another 4-2 two races later.
Eagles had luck on their side in heat eight when Hammers were on a 5-1.
Richard Lawson, in second place, suffered an engine failure which forced Cameron Woodward to fall and the race was awarded as a 3-3.
Cook, guesting for the injured Davey Watt, top-scored for Lakeside.
Eagles: Pedersen 11+2 (5), Newman 11+2 (5), Kylmakorpi 8+1 (4), Lahti 7 (4), Woodward 6+1 (5), Michelsen 5+2 (4), Halsey 2+1 (3).
Lakeside: Cook 11+2 (5), Bridger 8 (5), Lawson 6 (4), Nilsson 6 (4), King 4 (4), Ellis 4 (5), Morley 1+1 (3).
- Video: Watch the highlights of Albion's 3-3 thriller at Norwich
- Albion boss wants to sort out spot kick duties
- Video: Watch the highlights as Crawley hit back from two goals down to secure a draw
- Beer admits "kick up the backside" helped him to new Sussex deal
- Whitehawk to host Bognor in Senior Cup