Mark Warburton's team raced into a two-goal lead after Lee Wallace and Barry McKay both netted inside the opening 33 minutes.
Cowdenbeath pulled one back with an exquisite Dean Brett free-kick just before the break but Waghorn claimed the match ball with three second-half goals - including two penalties - as Rangers booked their place in Monday's fifth-round draw.
The former Wigan forward has now overtaken Peterhead's Rory McAllister to become Britain's top scorer in all competitions this season with 25 goals from 27 games.
Warburton disappointed those in the 20,000-strong Ibrox crowd eager to see new signings Harry Forrester and Maciej Gostomski by naming the pair as substitutes.
The Blue Brazil knew they would be up against it against the Championship leaders but hoped 14-goal striker Greig Spence might be able to pinch another goal against Rangers just as he did when he helped former club Alloa knock them out of last season's Petrofac Training Cup.
But it was clear from the outset the hosts were never going to be tested. Waghorn and Kenny Miller both came close before the breakthrough arrived after 19 minutes.
Gedion Zelalem's ball from wide into Waghorn's feet was cushioned to the feet of strike partner Miller. The former Scotland international did well to look up and spot the run of Wallace, playing a perfect pass for the left-back to run on to before slotting through Jamie Sneddon's legs for the opener.
Rangers - purring again after back-to-back wins over Hibernian and Dumbarton re-established Warburton's men as the Championship promotion race leaders - then added a second as McKay sped away from Brett, cut inside right-back Bradley Donaldson before sweeping a perfect finish across the goalkeeper.
There was a setback four minutes before half-time when Dom Ball's foul on Spence just outside Rangers' box presented Cowdenbeath with a free-kick chance. Brett took it in style as he clipped a precision set-piece off the underside of Wes Foderingham's crossbar and into the net.
But it took just three minutes of second-half action for Warburton's men to pull away again. Zelalem flicked a Miller pass into Waghorn's path and the bullish Englishman held off Fraser Kerr before driving a fierce strike over Sneddon.
When Kerr brought down James Tavernier as the full-back drove into the box in the 56th minute Waghorn was able to put memories of his recent penalty miss against Falkirk to rest by stroking home the fourth from the spot.
Forrester was handed his debut soon after but it was a relatively quiet introduction.
Waghorn had time for one last cheer though as he rounded off his treble with another penalty with 12 minutes left after the galloping Tavernier was again brought down inside the penalty area, this time by Chris Kane.