The home side were missing Stephen Hughes from the midfield after he tore a hamstring against Celtic on Saturday.
But Jim Paterson and Paul Quinn recovered from knocks they picked up during that defeat to face Walter Smith's men and Phil O'Donnell came in to replace Hughes.
Chris Porter dropped to the bench, as Marc Fitzpatrick joined Ross McCormack up front.
Boyd came back into the starting eleven for Rangers, having been on the bench for recent important matches in the Premier League and the Champions League.
The first half was notable for the sound of referee Iain Brines' whistle.
Both sides have shown how well they can pass the ball this season, yet a series of niggly fouls and over-officious refereeing hampered the flow of the game.
Rangers captain Barry Ferguson almost gave the Ibrox side the perfect start when he hit the post with a free-kick 20 yards out.
On 18 minutes, Motherwell midfielder Paterson put in a great cross which was met by Keith Lasley, but his effort went just wide of Alan McGregor's post
Four minutes later, Rangers took the lead when Boyd set up strike partner Novo, who smashed it into the net from ten yards for his sixth goal of the season.
Motherwell manager Mark McGhee was an animated figure on the touchline, believing a Rangers player had obstructed his goalkeeper.
Aside from Lasley's header, Motherwell's best chances came from Ross McCormack.
Ross McCormack troubles the Rangers wall with a free-kick
The former Rangers striker launched a series of free-kicks, the best of which went under the visitors' wall, but McGregor scrambled to get his body behind it.
Shortly before the interval, Rangers boss Smith ran out of his dugout and on to the pitch to vent his fury at Brines' decision not to award Rangers a penalty after Novo had been upended by keeper Smith.
Motherwell started the second half with a sense of purpose and looked the livelier side.
However, Rangers doubled their advantage when they broke up the park in 53 minutes. Novo fed Boyd from the inside left channel and he drilled the ball the net under Smith from 12 yards.
The Steelmen brought on Porter for Lasley but all too often their striking trio struggled to find a way past David Weir and Carlos Cuellar.
They did have Rangers rattled in the final quarter of the match, as first a volley by Stephen McGarry and then a drilled shot by Stephen Craigan put the pressure on McGregor.
In the final minute of regulation time, Quinn pounced to lash home from six yards to grab a consolation goal for Motherwell.
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