Dobra sent an early effort wide for the hosts after dispossessing Sam Ling, with Nik Tavares picking up a yellow card moments later.
The home side remained on top, but Phipps produced a vital block on 12 minutes to deny a goalscoring opportunity.
Ryan Hill was denied by a great save on 17 minutes, then created a great chance for Josh Rees after breaking up play and driving into the box, but his teammate could not profit.
But Rees produced an emphatic finish when Hill’s dangerous delivery was flicked on five minutes before the break to give Daggers the lead.
Frank Vincent joined Tavares on a yellow card on 52 minutes, but Daggers were reduced to 10 men with 20 minutes left when Phipps was dismissed for pulling Grigg back.
And Chesterfield made their extra man count almost immediately as Ryan Colclough levelled.
Loan signing Aidan Francis-Clarke came on for his debut in place of goalscorer Rees, with Lewis Page making way for Flynn Clarke soon after.
Conor Lawless replaced Omar Mussa with nine minutes left, but the hosts were awarded a late penalty which Will Grigg converted.
And Oliver Banks added a third in the seventh minute of stoppage time to rub salt into the wounds for Daggers, ending their three-match winning run.