His 64 set up a six-wicket win over Rolleston in the first round at Queen's Park.
But an even more impressive 55 against Belper Meadows later in the day proved in vain as the visitors edged home by one wicket off the last ball.
Rolleston started well after winning the toss and raced to 82-1 in the 11th over.
But then Zaroob held a well-judged low catch at long on to dismiss Louis Burrows for 42 and Chesterfield took charge.
Harry Wilmott, Reece Johnson and Matt Taylor claimed two wickets apiece to restrict Rolleston to 137-8.
Zaroob opened and soon put Chesterfield ahead of the run rate, hitting three leg-side sixes as he stormed to 64 off 43 balls before he was caught at long on off a skier.
That made Chesterfield 93-4 but Ben Kingham ensured victory with 10 balls to spare, striking several powerful blows in his 35 not out.
Zaroob was in dazzling form in the second game.
This time he did most of his scoring on the off side, repeatedly smashing the ball through and over the field.
At one stage he hit 11 fours off 16 balls he faced and several of his boundaries cleared the rope on the first bounce.
He was caught at the wicket for 55 off just 25 balls but Chesterfield did not make the most of the flying start.
Luke Westwell scored a fine 43 but no-one else reached double figures as they closed on 140-7.
Belper lost three early wickets but looked on top until off-spinner Kemira Wijenayake (4-20) took a wicket in each of his four overs to reduce them to 106-7.
They needed 11 off the final over with two wickets left and, with the scores level, Jordan Lemon ran out Alfie Kelly at the bowler's end off the penultimate ball.
That left the well-set Chris Whiteley (25 not out) on strike and he hit the last delivery to the leg-side boundary to clinch Belper's win
Chesterfield seconds lost by four wickets to Belper Meadows in Derbyshire League Division Three North at Queen's Park.
Opener Eddy Allcock drove crisply in his 36 after Chesterfield were put in but, despite Callum Hiron making 40, they struggled to accelerate as they made 192-8 off 45 overs.
Opener Chris Henson's rapid 58 put Belper in charge and, although Adam Woodhouse took 3-40, they won with eight overs to spare.
Chesterfield are 11th of 12 in the table but have a game in hand on most of their rivals.
The third team drew at Calow and stay top of Nine North.
They scored 190-8 off 40 overs and held Calow to 160-8, Charlie Robinson taking 4-12.
Chesterfield's Sunday side lost by 150 runs in the Mansfield & District League at Eckington where they were bowled out for 78.
Chesterfield have.a double-header in the League this weekend, hosting Ockbrook & Borrowash at Queen's Park on Saturday and Cutthorpe on Sunday.
Also on Saturday, the seconds travel to Langley Mill United and the third team play Whittington Wanderers seconds at Calow.
The Mansfield League side are at Grassmoor Works on Sunday