It's the third time Dale have progressed to this stage of the competition in four years.
Henderson headed home Steven Davies' corner in the 17th minute, whilst Conrad Logan had to make a fine double save midway through the first half.
Rochdale missed a number of chances early in the second period, but Henderson made sure of Dale's place in the next round just after the hour mark with a composed finish from Oliver Rathbone's through ball.
Harrison McGahey came in for the injured Joe Bunney, with Joe Rafferty moving to left-back. Steven Davies also returned to the starting eleven, in place of Joe Thompson.
Dale could have been ahead inside the opening ten minutes.
A break through the middle from Callum Camps saw Rafferty played in on the left side. His delivery rolled across the six yard box teasingly, before being turned behind for a corner at the far post.
The hosts, buoyed by a sell out crowd at the Furness Building Society Stadium, were testing Dale's defending at set pieces early on. Conrad Logan, having signed a contract until the end of the season this week, was keeping Barrow at bay early on.
Calvin Andrew saw a left foot shot from outside the area deflected behind for a corner, from which Dale took full advantage.
Davies' out-swinging delivery was met by Henderson, who directed a header into far bottom corner to put the visitors ahead.
An opening early goal is exactly what Keith Hill would have wished for, which Davies tried to double minutes later with a turn and shot which flew over the bar.
The home side's best chance of the first half came midway through. A ball over the Dale defence fell to Richard Bennett, whose shot was saved by the legs of Logan. The rebound fell to centre-back Moussa Diarra, but Logan held on to his follow up.
Oliver Rathbone sent a shot on the turn wide, after Andrew had found him inside the area, but an even better chance fell to League One Player of the Month for December Matthew Lund a minute later.
He jinked his way into area from the right side and came one-on-one with goalkeeper Jon Flatt, but his left footed effort drifted past the far post.
Andrew did test Flatt when he headed McGahey's down into the ground, which the stopper held at the second attempt.
The home side again troubled from a set piece which was partially cleared before being headed back into the area, but Diarra sent his flick on wide of Logan's left post.
The final chance of the half fell to Dale, when Rafferty broke into the area from the left and squared for Lund, whose effort was scrambled wide for a corner.
After the break, Barrow upped their energy in an attempt to haul themselves level early on. However, it was Dale who were creating all of the goal scoring opportunities.
Davies sent a free-kick just wide of goal, before a counter attack and subsequent pull back from Camps found Lund, who also sent his shot off target.
Another swift counter attack a minute later was led by McGahey who found Camps. This time the Dale skipper found Davies, who became the third in quick succession to fire wide.
Fortunately for Dale, Henderson was much more clinical just after the hour mark when he doubled Dale's advantage. A fine through ball from Rathbone found Henderson one-on-one with Flatt, and he finished calmly in front of the travelling Dale supporters.
The goal appeared to knock the stuffing out of Barrow, as Keith Hill's side continued to control the game in the final 25 minutes.
Logan held a header from Bennett with a rare second save, whilst Rathbone fired over from 20 yards as Dale went in search of a third.
Andy Cannon, Jamie Allen and Niall Canavan all made substitute appearances in the final ten minutes, as Henderson, Rathbone and Keith Keane made way respectively.
Dale were comfortable as the game came towards a conclusion. Lund had a shot tipped wide which was given as a goal kick, but the final chance fell to the home side. Jordan Williams sent a low ball in to Byron Harrison from the left, but the striker turned his effort wide.
A thoroughly professional performance from Keith Hill's side, who now await Monday night's FA Cup fourth round draw.