The Light Blues fell behind in the contest inside 20 minutes when Matty Kennedy scooped an effort against James Tavernier which cruelly snuck in at the near post.
The visitors were indeed reduced to ten men when Joe Wright was given his marching orders for denying an obvious goalscoring opportunity, but Tavernier failed to capitalise from the spot when his penalty was thwarted by Will Dennis.
However, the Ibrox side rallied to net an equaliser on the stroke of the half-time interval through Fabio Silva, before Ben Davies and Tom Lawrence, both introduced as second half substitutes, turned the game on its head and John Souttar rounded off the scoring in stoppage time.
Speaking to RangersTV after the victory, the Gers boss said: “Kilmarnock are a difficult opponent and they have only lost twice since December 3rd, both times against us.
“In that way, it’s massive to get the three points.
“We had a really good start, but you need to get the ball over the line.
“I thought we should have had a penalty for a clear handball and VAR asked the referee to come to the screen to show something was wrong.
“The referee made another decision, but you need to stay focussed and not to become angry or give up. Then a few minutes later, we concede a goal out of nothing.
“The team showed resilience and what I demand of them, to never give up, and we’ve had a lot of games this season where we’ve changed the situation.
“That’s what we continued to do and we pushed to get the three points.”
Rangers were indebted to their substitutes bench for providing impetus in the second period, with Davies showing tremendous opportunism to follow up on John Lundstram’s strike while Tom Lawrence found the top corner with a rasping strike moments later.
The impact from the bench underlined the strength in depth at Clement’s disposal, which the Light Blues boss hopes will bear fruit for the side as they enter the final three league outings of the campaign.
He added: “We needed more urgency in our passing, to play forward more, and take more risks in the final third without the ball.
“That’s what we done in the second half and you saw our game become better.
“We got the chances and scored a couple of really nice goals.
“It’s been the same over the last couple of months: players fighting to be in the starting lineup but being ready when they’re not starting in order to make the difference.
“A lot of times you can make the difference in the second half when the opponent becomes tired and the fresher players come in with all their power.
“We need to continue in that way like the last couple of months. It’s not the first game like that, but it’s been the same thing with several players.
“We need to continue the unity and collective work to get the three points.”