Dewsbury battled back superbly from 22-10 down and looked to be on course to secure a draw following tries by Dale Morton and Shane Grady.
However, the Rams were denied at the end as a brace of tries in the closing stages from Jonathan Pownall, saw the Centurions edge it 30-22 and stretch their winning run to 17 straight matches.
Leigh took an eighth minute lead when Ryan Brierley gathered Martyn Ridyard’s kick to score his 27th try of the season, with Ridyard converting.
Dewsbury were unfazed by the league leaders though and hit back to level when in-form centre Shane Grady scooped up a loose pass and raced over for the try, which hooker Tom Hemingway converted.
Ridyard was again involved as Leigh regained the lead when his kick allowed Liam Kay to score.
Again Dewsbury responded superbly as they piled on the pressure.
Hemingway’s short kick forced the Centurions to drop-out and after the home side then conceded a scrum, the Rams struck when Scott Hale was on the end of a move to race in at the corner and send the sides into half-time level at 10-10.
Winger Kay grabbed his second of the match and 22nd try of the season two minutes after the re-start, with Ridyard converting from wide out.
Dangerous substitute Sean Penkywicz made a darting run and sent Tommy Goulden over, with Ridyard’s goal giving the Centurions a 12-point lead.
Dewsbury gave themselves a lifeline when Morton raced in at the corner nine minutes from time and Hemingway landed a superb touchline goal.
Grady struck with his second try and Hemingway held his nerve to level with the conversion.
A knock-on from the kick-off was capitalised on as Leigh attacked and Pownall gathered Ridyard’s kick to score.
Dewsbury attempted a short kick off but it didn’t pay off and Leigh fans breathed a huge sigh of relief when Pownall crossed for a quickfire double as the hooter sounded.