Owen Coyle's side suffered a chastening opening-day defeat against his former employers Burnley, but they recovered from a lacklustre first hour to see off Derby at the Reebok on Tuesday night.
Debutant Conor Sammon should have given the Rams an early lead and, although Marvin Sordell went close at the other end, Bolton departed to boos at the interval.
Nigel Clough's men were quickest out of the blocks once again after the interval, with Nathan Tyson going close before Richard Keogh's strike from a corner was ruled out for a foul.
Following a spell of persistent Wanderers pressure, Davies finished legally from a corner and Eagles made sure of the points - but not until Derby substitute Mason Bennett had rattled the post.
Matt Mills made his Bolton debut at centre-back and Eagles got the nod on the left wing as Tim Ream and Martin Petrov dropped to the bench.
Sammon came straight into the Derby attack at the expense of 17-year-old Will Hughes after joining from Wigan yesterday, while James O'Connor was handed a first start in defence with Jake Buxton laid low by illness.
Sammon had the opportunity to make perfect start in the third minute when he burst through on goal but could not fully shake the attentions of Mills and shot tamely at Adam Bogdan in the Bolton goal.
Wanderers widemen Eagles and Lee Chung-yong responded with speculative efforts in quick succession, although the latter then wildly slashed a shot out for a throw.
Eagles' aim was truer in the 18th minute when his pinpoint cross found Sordell, but the Team GB striker headed wide when well placed.
The half took on a disjointed feel from that point and anxiety in the Reebok Stadium stands momentarily spread to the pitch as Bogdan fumbled Jamie Ward's corner, prompting a scramble concluded by Keith Andrews' clearance.
Derby saw a golden chance slip shortly after the restart when Mark Davies produced a goal-saving tackle to deny Nathan Tyson with the goal at his mercy.
From the resulting corner Rams defender Richard Keogh had the ball in the net as Bogdan flailed once more, but referee Craig Pawson spotted an infringement.
Sordell and Eagles troubled the visitors goal as Wanderers looked to respond and the former made way for Benik Afobe with an hour gone.
The on-loan Arsenal youngster almost made an instant impact when he forced a superb fingertip save from Derby's Frank Fielding after latching on to Davies' delicate chip.
That chance prompted waves of Bolton pressure and although Fielding made another excellent reaction save from Eagles, he was forced to pick the ball out of his net in the 76th minute.
Eagles' left-wing corner fell invitingly and Davies made no mistake, slamming home emphatically.
Another uncertain Bogdan moment followed as Bennett's drive squirmed under his dive and against the post.
But Coyle and co could breath easily early in stoppage time when Eagles forced his way through a pair of challenges to slot an assured low finish.