The victory leaves them 13 points adrift of runaway Scottish Championship leaders Hearts but, more importantly, moves them six clear of third place Hibs who drew 1-1 at Tynecastle earlier in the day.
Jon Daly, Lee Wallace and Dean Shiels were on target for the Glasgow giants who were forced to fight back from a goal down after quarter-of-an-hour.
From Chris Turner’s corner to the far post, the ball was headed back by Colin Nish for Andy Graham to finish off from close range and give the visitors a deserved lead – and they were on course for their first win over Rangers since 1894.
And The Sons almost doubled their advantage a few minutes later when a 12-yard header by the unmarked Nish was saved by home keeper Steve Simonsen.
However, the hosts were level on 22 when Steven Smith’s cross took a deflection into the path of Daly who equalised from 10 yards.
As the Gers began to take control, Smith and Daly both had efforts saved by Daniel Rogers.
The second Rangers goal arrived four minutes before the break when Smith was again the provider, this time for Wallace who smashed the ball into the bottom left-hand corner of the net from the edge of the box.
Although Dumbarton continued to threaten the home defence during the second half, they were unable to get the ball past Simonsen.
Christopher Kane and Nish had efforts shortly after the break while Kenny Miller went close on a couple of occasions for the hosts.
Kyle Hutton, David Templeton and Smith were also off target for Rangers who, despite enjoying greater possession, made heavy weather of trying to kill off the minnows from just up the River Clyde.
Nicky Clark came close to notching a third goal for Rangers less than a minute after coming on as a 74th minute substitute when his shot from a tight angle was well saved by Rogers.
Kane had three late efforts as Dumbarton searched for an equaliser but deep into injury time, Rangers grabbed a third – which made the scoreline slightly flattering – when 81st minute substitute Shiels located the bottom left-hand corner of the net from Clark’s assist.
As for the hosts, they will have play better in their next home fixture in 13 days’ time when leaders Hearts travel to Ibrox where anything but a Rangers victory will probably signal the end of their chances of earning automatic promotion back to the top tier of Scottish football.