The Robins had not won away from the LCI Rail Stadium since February – but that unwanted record was crushed in emphatic fashion thanks to in-form hitman Eisa.
Kyle Storer and Brian Graham had both gone close to open the scoring in Derbyshire before Eisa swept home his seventh goal of the season from the edge of penalty area just before the break.
Eisa then curled home a delightful second, after being brilliantly set-up by substitute Danny Wright, as the Robins continue their fine run of form that has seen them collect three wins in the last four games.
Manager Gary Johnson made one change to his starting line-up with Jerell Sellars replacing Kevin Dawson, who missed the game with a knee injury. Jordan Cranston returned on the bench.
Sellars was bright in the opening minutes as he popped up on both flanks to receive the ball and drove at the home defence before freeing Storer, who in turn fed Joe Morrell to fire in a blocked shot.
Graham then intelligently slid in Storer who, clean through on goal, saw his shot blocked by the legs of goalkeeper Tommy Lee as he rushed off his line to deny the captain.
Jordan Flores fired high over the bar for the hosts, after impressive build-up play down the right flank from Scott Wiseman, as the home crowd looked to roar their team on with new manager Jack Lester pitch-side.
Eisa threatened down the wing with a powerful direct run, and the resulting corner was headed just wide by Graham from Morrell’s pinpoint delivery.
The home side had their best chance of the match when Ian Evatt shot wide of the target, after a ball in from the left caused problems for Jamie Grimes and Scott Flinders and fell to him 15 yards out.
Flores then hit a wicked shot from 18 yards out that swerved and dipped in front of Flinders who did well to shovel the ball over the bar.
Pell skilfully drove up the middle of the park with a trademark surge, shrugging off two tacklers, and Eisa headed wide before the in-form striker took a chance seconds later in typically clinical fashion.
The forward had little on when took aim from 20 yards out, after receiving the ball from Sellars, but he beautifully bent his shot low into the bottom left corner for the opening goal and half-time lead.
Eisa threatened again at the start of the second half, finding the side netting as he looked for the near post after being sent clear down the left by Pell.
The all-action Pell then had large appeals for a penalty waved away after falling under a heavy challenge after he was freed by Winchester’s incisive pass.
Chesterfield were still looking for a way back into the game, Storer producing a fine block to deny De Girolamo as he pulled the trigger close to the penalty spot.
Substitute Danny Wright immediately made an impression as he won a knock down for Eisa to fire over before the pair combined again, with Wright turning a cross onto the left-hand post with the offside flag up.
The duo then linked-up in devastating fashion on 69 minutes when Wright turned a long ball forward into the path of Eisa who picked his spot and curled into the bottom right corner.
Morrell could have made it three, after Sellars glided past two men out wide, but his shot lacked the power to beat Lee.
Sellars then fired over with minutes remaining before Freddie Hinds was denied by Lee in injury time as the Robins comfortably held on to record a crucial victory.
CHESTERFIELD: Lee, Hird, Wiseman, Evatt, Dennis (Ugwu 56), O’Grady, De Girolamo, Flores (Mitchell 56), Reed (McCourt 76), Weir, Briggs. Subs not used: Anyon (Gk), Rowley, Sinnott, Kellett
CHELTENHAM TOWN: Flinders; O’Shaughnessy (Cranston 45), Grimes, Moore, Winchester, Pell, Morrell, Storer, Sellars, Eisa (Hinds 82), Graham (Wright 62). Subs not used: Flatt (Gk), Atangana, Boyle, Davey.
REFEREE: Ben Toner
ATTENDANCE: 5,305 (217 from Cheltenham)