Rangers began the match nervily with Dumbarton pressing, but the home side soon got a foothold and took the lead through captain Lee McCulloch after 15 minutes.
Darren McGregor then doubled Rangers' lead after 30 minutes of play with a right-footed strike at the near post as the home side began to look comfortable.
Kris Boyd then set up Nicky Clark's goal just nine minutes into the second half to all but win the match for Rangers as Dumbarton were beginning to tire.
Rangers were comfortable and began to show it with some confident attacking football as the match entered the final 20 minutes.
The home side were keeping the pressure up at Ibrox and it eventually paid off after Chris Turner put the ball into his own net from a corner with 15 minutes remaining to make it 4-0.
Dumbarton refused to give up though, and they pulled a consolation back through Bilel Mohsni's own goal with just nine minutes remaining.
Rangers stood firm to deny Dumbarton as they remain at the foot of the Scottish Championship.
Dumbarton have now failed to beat today's opponents in their previous 43 attempts.