The lead changed hands throughout the first 20 minutes, with Willem de Waal's boot keeping the visitors in the game.
However, a magnificent try from Killian, who stole clear from 30m out in the eighth minute, backed by accurate kicking from Jantjies, who was successful with 10 attempts at posts in the match, put the hosts 10-9 ahead midway through the first half.
Western Province countered with a burst of aggression, and after swinging the ball well back and forth, camping on the Lions tryline, right wing JJ Engelbrecht went over in the 23rd minute to give the visitors a 14-10 lead after De Waal‘s conversion attempt deflected off the right post.
And four minutes later Province scrum-half Dewaldt Duvenage broke clear with a magnificent run, offloading to eighth man Duane Vermeulen who dotted down, and De Waal made up for his earlier miss to give them a convincing 21-10 lead.
Jantjies, however, kept the Lions in the hunt with three successful penalties before half-time to bring the hosts within two points at 21-19.
The visitors displayed another burst of energy shortly after the break, swinging it both ways before replacement Conrad Hoffmann went over on the left wing, with De Waal again converting and stretching the gap to 28-19.
But Jantjies was superb and wasted no chances, adding three points with every chance he got, and reduced Province's lead to 28-25.
In the 61st minute Lions eighth man Warren Whiteley chipped clear from 40m out, chasing the ball all the way to the line before he fumbled it going over. Killian, however, picked up the loose ball to score his brace and regain the lead for the hosts.
Just three minutes later, Killian was again on the prowl, sprinting 80m down the left wing from his team's own tryline before passing to Derick Minnie who dotted down.
Jantjies converted both tries and the home side were suddenly in control, having built an 11-point margin at 39-28. For good measure, Jantjies went over in the 76th minute and fittingly converted his own try to seal the lid on a solid performance.
While the Lions have closed the gap on the top four on the log, Province are flailing, and after losing three games in succession, they will be desperate to regain the form that saw them nestled in second place before the weekend.
Lions: Tries: Michael Killian (2), Derick Minnie, Elton Jantjies. Conversions: Jantjies (4). Penalties: Jantjies (6).
Western Province: Tries: JJ Engelbrecht, Duane Vermeulen, Conrad Hoffmann. Conversions: Willem de Waal (2). Penalties: De Waal (3)