Jennings shrugged off an ongoing Scottish Football Association probe into betting patterns surrounding his red card against Hearts last month to cap an assured performance with a late headed goal at Dens Park.
McCall's revamped strikeforce had given Motherwell the perfect platform as the recalled John Sutton netted early in each half against an enthusiastic Dundee side.
Jamie Murphy was rewarded for a vibrant display with a solo goal in the 87th minute to round off the scoring.
Dundee hit the bar shortly after Sutton's second through a deflected free-kick from Leigh Griffiths but he was sent off in the closing stages to complete a forgettable afternoon for the hosts in the fourth-round clash.
McCall had lost the strikeforce that started his first match in charge, a goalless derby at Hamilton, after Alan Gow and Nick Blackman both left the club, and he was also without the injured Steven Saunders.
But the recalled Sutton continued his decent goalscoring record for Motherwell with the aid of two assists from Murphy, who started on the left of a three-pronged attack with Humphrey on the right.
Jennings returned from a three-match ban, while Marc Fitzpatrick started in midfield as he looks to earn a new contract.
McCall had admitted Dens Park looked the most likely venue for a fourth-round shock with First Division side Dundee having conceded just one goal in a six-match winning streak and Motherwell without a victory in six.
But his side took a firm grip on the early proceedings with Sutton netting against his former club following a simple but well-executed move.
Jennings found Murphy's run down the left channel with a free-kick from near the halfway line and the Scotland Under-21 international cut it back for Sutton to slot inside Rab Douglas's near post.
Dundee struggled to cope with the visitors' forward running in the opening 20 minutes and Humphrey came close to carving out more chances.
The hosts settled down but Griffiths was flagged offside, to the disgust of the home fans, at the end of the two most promising first-half moves, and Darren Randolph held on to Gary Irvine's looping header following a short corner.
McCall's side twice came close to a second in the latter stages of the half. Douglas blocked Sutton's close-range header on the line following Stevie Hammell's corner and Murphy's low cross just failed to fall for Humphrey after good skill on the left.
But Motherwell netted two minutes into the second half thanks to the same combination.
There appeared little danger as Murphy ventured forward but Dundee failed to track Sutton's angled run and the flag stayed down after the youngster had flicked the ball through.
The Englishman got the ball under control and slotted home with his left foot into the far corner.
Dundee almost equalised two minutes later when a deflection on a Leigh Griffiths shot looped the ball over Randolph, but the ball bounced off the bar and outside the goal before Mark Reynolds headed away.
Motherwell repelled the pressure, which did not last long, and Dundee's frustration was evident when Sean Higgins felled Stephen Craigan with a late tackle, which sparked a confrontation that also saw Jennings, Randolph and Dundee midfielder Gary Harkins booked.
Motherwell regained control and Murphy shot just wide from 30 yards before the unmarked Jennings headed tom Hateley's cross into the corner of the net in the 81st minute.
Murphy's pace then took him past two men on the left-hand side before slotting home in the 87th minute.
Griffiths then saw red for a needless two-footed challenge on Hammell.