Opener Cox thumped six sixes on his way to making 100 from 122 balls after the hosts had won the toss and chosen to bat.
Smith then hit four maximums and 18 boundaries in all as he posted an unbeaten 129 from just 134 balls, their efforts ensuring Wombourne completed their 50 overs with an imposing total of 335-6.
It was a target which always looked beyond Hammerwich, particularly after David Hemmings had removed openers Brian Fisher and Richard Instone cheaply.
Skipper John Jennings showed admirable resistance with an unbeaten 68 but wickets continued to tumble around him, Jack Bradley and Ben Thomas both taking three each as the visitors were bowled out for 185.
Victory meant Wombourne sit fourth in the Premier Division and can currently claim to be ‘best of the rest’, 39 points behind the so-far dominant trio of Lichfield, Milford Hall and Tamworth, who all claimed convincing wins once more.
Leaders Lichfield, who host Wombourne this weekend in what is already a key fixture for the chasing pack, remain two points ahead of their closest challengers after a comfortable six-wicket win at Fordhouses.
Jem Stack hit 68 to ensure the hosts, wobbling at 21-3, posted a respectable 189-7 batting first.
But though Chris Guest then removed Lichfield opener Rich Taylor-Tibbott with the first ball of the reply, the visitors found it relatively straightforward going from then on, thanks in large part to Brinder Phagura’s 68 and a brisk 50 from 51 balls from Stuart Fielding.
While both were dismissed in quick succession, they had already done enough to put their team within striking distance of a target chased down with more than 15 overs to spare.
Defending champions Milford Hall sit second after making similarly light work of a chase against Penkridge.
Late hitting from visiting skipper Laeq Chisti (33 not out) at least ensured his bowlers had something to work with as Penkridge closed on 162-7.
Yet while Milford lost opener Dominic Afford cheaply, partner Waqar Saleem’s run-a-ball 76 ensured the chase was relatively comfortable, the home side reaching the target in 31.1 overs.
The win was Milford’s sixth in eight matches and their record is identical to third-placed Tamworth, who blew away Old Wulfrunians Tettenhall in a game which lasted just 34.1 overs.
Old Wulfs’ innings took up 22 of them, Matthew Coles claiming 6-12 as the home side were bowled out for just 57, with seven batsmen failing to score. Tamworth needed just 73 balls to chase down the runs.
Rugeley remain bottom of the table after falling to a 30-run defeat at home to an improving Brewood.
In a victory very much a team effort, no batsman passed 50 but several made valuable contributions as the visitors racked up 266-7 from their 50 overs.
Will Marsh then claimed three wickets, with Dean Lones, Tim Maxfield and John Redrup taking two apiece as the hosts fell short despite Ali Fawcett’s 62 and some entertaining late hitting from Luke Clark (52 from 25 balls).
Beacon sit fifth in the standings, albeit some 59 points off the top, after a seven-wicket win over Wolverhampton seconds.
Mike Hartwell claimed three wickets, including the key scalps of Rahul Kaushal (40) and Archie O’Hara (32) as the visitors collapsed from 81-1 to 156 all out inside 40 overs. Josh Pistorius and Jake Cartwright also took two wickets each.
A blistering 81 from just 61 balls from opener James Fildes then made the run chase comfortable for the home side. South African overseas ace Pistorius backed up his effort with the ball by making a patient 32 in support as Beacon reached their target in just 23.5 overs.
Next up for Beacon is a trip to Brewood, while Milford Hall visit Hammerwich and Fordhouses will aim to pull off a shock away to Tamworth.