Russell converted after a 53rd-minute corner and Goodwillie netted in the final seconds to move the home side level on points with Motherwell in mid-table in the SPL.
Motherwell failed to hit the heights of their 4-0 Scottish Cup win at Dundee on Sunday, although Chris Humphrey was denied an equaliser only by an excellent late save from Dusan Pernis.
Their lacklustre performance highlighted the need to strengthen after Marc Fitzpatrick followed Alan Gow and Nick Blackman in leaving the club since McCall took charge two weeks ago.
Ross Forbes replaced the long-serving midfielder, who rejected a contract extension, but the Motherwell bench lacked experience with the largely untried Esteban Casagolda the only outfield player over the age of 20.
United welcomed back Goodwillie from suspension and Jon Daly recovered from a groin strain to keep his place, but Barry Douglas dropped out with a head knock.
David Robertson came in for Scott Robertson, while Craig Conway made a late comeback off the bench following knee surgery.
United started well and Russell could not have come closer to giving them a fourth-minute lead from almost 25 yards.
Goodwillie's flick stretched the Motherwell defence and Russell hit an instant strike with the outside of his left foot, but it bounced off the inside of the post and away to safety.
United kept coming forward and Morgaro Gomis had a decent chance from the edge of the box but screwed his volley well wide.
Prince Buaben came much closer following a good flick by Russell but Darren Randolph brilliantly tipped away his powerful 20-yard strike.
The hosts continued to create half chances with Randolph recovering to save after Goodwillie had taken the ball round him before being beaten by the angle.
Motherwell's wide attackers, Jamie Murphy and Chris Humphrey, were being pushed back to give their formation the look of a 4-5-1, and Buaben was pushing up on the influential Steve Jennings.
But the visitors came into the game around the 20-minute mark. Murphy cut inside and shot narrowly wide from 20 yards before John Sutton volleyed well over from the edge of the box following a poor headed clearance from Keith Watson.
Randolph repelled two long-range efforts from Gomis either side of a mazy run from Murphy, which ended with a shot straight at Pernis and both sides cancelled each other out as the half progressed.
Motherwell survived two scares five minutes after the break after being put under pressure by a poor pass from Stephen Craigan.
Randolph could only palm out Russell's low cross but Stevie Hammell saved a certain goal by blocking Buaben's follow-up.
Paul Dixon soon went down under Humphrey's risky penalty-box challenge, but referee Iain Brines booked the United left-back for diving in what looked a harsh decision.
However, United soon took a 53rd-minute lead when Russell headed in off the post from six yards after Garry Kenneth had headed Dixon's deep corner back across goal.
The hosts had an initial lift from the goal, passing the ball around with increased confidence, before retreating.
But Motherwell were sloppy in possession when they reached the final third of the pitch and failed to put them under pressure.
Motherwell moved to a 4-2-4 formation after Jamie Pollock and Casagolda came on and they finally carved out a second-half chance with six minutes left.
Murphy got to the byline and crossed to the back post but Pernis blocked Humphrey's header on the line.
Goodwillie secured the points on the counter-attack in the last few seconds of the 90 minutes when he tucked the ball inside the post from 12 yards after being set up by substitute Stuart Armstrong.