The Titans had collapsed to 20 for five on the third evening as they chased 320 for victory, and it would have taken a remarkable rearguard action for them to save something from the match.
As it was the Lions took 31 overs on Sunday morning to wrap up the match, as the Titans were bowled out for 114.
Matshikwe got the ball rolling on the fourth morning when he picked up the wickets of Henry Davids and Roelof van der Merwe, while Leie bowled top-scorer Mangaliso Mosehle for 24 and finished the match when he had Ethy Mbhalati stumped.
In between Hardus Viljoen dismissed Shaun von Berg to grab his eighth wicket of the match, recording figures of 8 for 106.
The resounding victory put the Lions narrowly above the Cape Cobras at the top of the series table with 19.16 points, while the Titans took 4.38 points from the match.