The dismissal of Speers at 278 meant Greytown player-coach Mark Childs joined Rance and the winning runs were scored on the fourth ball of the 43rd over - a five-wicket win.
Andrew Fullerton-Smith and Jeremy Dean were the only Eastern Suburbs batsmen to top the half-century mark with opener Dean making 52 from 54 balls and Fullerton-Smith 51 from 52 balls.
Rance was clearly the pick of the Greytown bowlers both in wicket taking and economy, although Brian James would have been happy with his 3-51 from the full 10 overs. The conceding of 33 runs from wides suggests the accuracy was not always as good as it might have been.
Among the batsmen for Greytown, opener Jake Ross was solid enough in getting through to 27 from 48 balls, skipper Tim Lucas struck five fours in his 29 from 24 balls and Steve Coleman reached 26 from 27 balls.
Short scoreboard:
EASTERN SUBURBS 301 (Dean 52, Brodie 34, Johns 30, Gibson 2, Karaitiana 17, McLauchlan 41, Fullerton-Smith 51, Tugaga 12, Dry 2, Joseph 4 not out, Connell 8, extras 48; fall of wickets, 93, 118, 130, 145, 163, 244, 279, 288, 289, 301; Rance 9.5-0-36-4, G Reisima 9-0-59-0, Foster 8-1-72-0, Coleman 10-0-55-2, James 10-0-51-3, M Reisima 2-0-14-0) lost to GREYTOWN 302-5 (Ross 27, Lyttle 3, Lucas 29, Coleman 26, Speers 68, Rance 118 not out, Childs 9 not out, extras 22; fall of wickets, 27, 46, 85, 103, 278; Joseph 10-2-48-3, Connell 5-1-42-1, Tugaga 9-1-59-1, Gibson 8-0-63-0, Dry 6.4-0-44-0, Karaitiana 5-0-41-0) by five wickets.
Other first day results: Pukekohe-Metro (Northern Districts) 301-8 (Kevin Farrell 111, Ash Vonale 95) beat Suburbs-New Lynn (Auckland) 168 (Jeet Raval 54, Michael Bates 36; Vodnala 3-24) by 133 runs; East Shirley (Canterbury) 255 (Leo Carter 117, Tim Papps 52; Nick Beard 4-33, Michael Sneddon 3-33) beat Albion (Otago) 238 (JR Glenn 53, Nick Beard 49, Chris Harris 53, Tim Ford 45; Jared Roberts 3-51, Dexter Marsh 4-35) by 17 runs.