Skipper Curtis Woodhouse broke the deadlock on 25 minutes by converting from the penalty spot following a trip on Lee Tomlin.
Summer signings Alan Marriott, Gareth Jelleyman, Sagi Burton, Dean McDonald and Lee Phillips were all handed full league
debuts for Diamonds.
But the visitors made a sloppy start to the season as Burton conceded a corner after 10 seconds and Matt Crabb's cross hit Marriott in the stomach before the ball was cleared inside the six-yard box.
Former Diamonds striker Jean-Michel Sigere held off Burton and saw a shot held by Marriott. However Garry Hill's side battled back and gradually gained control.
Tomlin's 30-yard free-kick was gathered by Lee Hook and the teenager continued to pose plenty of problems to the home defence down Diamonds' right wing.
Another attempt by Tomlin was deflected wide and he twice went close again before the break. His initial shot was blocked and, when club captain Andy Burgess lofted the ball to the edge of the box, Tomlin's volley flashed wide of the far post.
Have your say on the match by posting your comment by registering at the blue button. Vote for the man of the match on the right of the screen. Email your thoughts by clicking hereEastbourne piled on the pressure in search of a second-half equaliser. But last season's Blue Square South play-off winners spurned a series of chances.
Sigere fired wide at the near post and then raced clear, only for Marriott to make a save and Jelleyman then headed off the line.
Marcus Kelly's 30-yard drive bounced off the top of the crossbar and Woodhouse was close with a long-range lob which went just over.
Diamonds had a lucky escape midway through the second period as substitute Simon Wormull went clean through. However the former Nene Park winger scooped his shot over the stand.
Chris Hope nearly doubled Diamonds' advantage late on. But Woodhouse's goal was enough.
Eastbourne: Hook; Austin, Pullan, Baker, Jenkins; Harding, Smart, Armstrong, M Crabb (Wormull 64); Atkin (N Crabb 65), Sigere (Tait 74). Subs not used: Lovett, Winterton.
Diamonds: Marriott; Osano, Hope, Burton, Jelleyman; Tomlin, Burgess (Corcoran 80), Woodhouse, Kelly (sub Gulliver 86); McDonald (Wolleaston 69), Phillips. Subs not used: Mitchell, Smith.
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