First-half goals from Salomon Rondon and Jay Rodriguez secured Albion’s safe passage to the fourth round and gave Pardew a first win in nine games since succeeding Tony Pulis at the end of November.
Albion could even afford the luxury of a Hal Robson-Kanu penalty miss just before half-time, the Welshman sending his tame attempt too close to Exeter goalkeeper Christy Pym.
West Brom had gone 21 games without a win since beating Accrington in the Carabao Cup in August, but Pardew’s most recent FA Cup memory was sending out a Crystal Palace side to contest the 2016 final.
Pardew named a strong side which was a reflection of his desire to spark some momentum into Albion’s miserable season.
But Jake Livermore started on the bench following his midweek altercation at West Ham, when a Hammers fan allegedly made a comment about the death of his baby son after he was substituted.
The ingredients were there for an upset with a heavy pitch and the vast majority of a sell-out 5,638 crowd desperate to see Exeter down top-flight opposition in the FA Cup for the first time since January 1981.
But West Brom ensured that romance was in short supply with one of the fastest goals of the season coming after just 70 seconds.
James McClean’s cross fell to Rondon and the Venezuelan’s firm sidefoot was too hot for Pym to handle.
The Grecians goalkeeper stopped Rodriguez and McClean from adding quickfire goals, but he had no chance when his defence let him down after 25 minutes.
Troy Archibald-Henville failed to clear and Dan Seaborne stood still as Rodriguez finished emphatically from close range.
Rondon and McClean almost scored before Albion were presented a gilt-edged opportunity to extend their advantage from the penalty spot.
Pierce Sweeney felled the energetic McClean but Robson-Kanu, on as an early substitute for the injured Kieran Gibbs, made a hash of the spot-kick.
Exeter were almost gifted a route back into the game in first-half stoppage time when Ben Foster fumbled Liam McAlinden’s cross.
But Jayden Stockley could only prod against the post when it was easier to score.
That near miss energised Exeter, however, and West Brom were put under pressure at the start of the second half.
Stockley’s free-kick floated wide, Foster was forced into a point-blank save from substitute Lee Holmes, and Ryan Harley also went close.
Robson-Kanu should have put further gloss on Albion’s win when he broke through and failed to trouble Pym.
It was a decent second-half showing from Exeter, but in the end their spirited resistance came to nothing.
Paul Huntington says Preston's play-off hopes this season hinge on them getting the balance right on and off the pitch.