The Lions had reached a commanding 264 for two when bad light stopped play at 4.15pm, with 25 overs still scheduled to be bowled, thanks to a great 108 not out from Cook after the visitors had won a good toss and elected to bat first on a brownish, dry pitch.
Cook has always brought a sober, methodical approach to opening the batting and he was content to let Rassie van der Dussen dominate the morning session, the youngster scoring an 84-ball half-century as the Lions went into lunch on 92 without loss.
The 32-year-old Cook did have a moment of rare celebration however when he became only the fourth batsman to score 10 000 runs in South African domestic first-class cricket, joining the hallowed trio of Graeme Pollock (12 409), Peter Kirsten (11835) and his own father, Jimmy Cook (11307).
Playing the anchor role suits Cook just fine and he brushed off being dropped the ball before lunch on 32 by Heino Kuhn at slip off left-arm spinner Roelof van der Merwe, as well as the departure of Van der Dussen, top-edging a hook off Rowan Richards, and being well-taken by Junior Dala running round from fine leg, for 65.
Cook and Van der Dussen had opened the innings with a stand of 114 off 230 balls and the captain and young Dominic Hendricks then added 115 for the second wicket in just over two hours, off 158 deliveries.
Hendricks played a dashing innings, hitting 11 fours and a six in his 63 off 87 balls before he pushed at a Richards delivery outside off stump and wicketkeeper Mangaliso Mosehle took a good diving catch.
Cook and McKenzie then took the Lions through to stumps, with the centurion having batted for five-and-a-quarter hours and faced 211 deliveries.
It was a messy bowling display by the Titans and a top-class batsman like Cook duly capitalised, stroking 11 fours and seldom looking threatened.
Richards may have claimed a pair of wickets, but it came at a cost of more than four runs an over for the left-arm seamer, while Dala produced a barrage of short-pitched bowling on a placid pitch.
JP de Villiers also conceded a lot of boundaries, including four in one over by Hendricks as the left-hander brought up the 150.
Van der Merwe, who should have removed Cook on the stroke of lunch, was the best of the Titans bowlers, but the weather certainly saved the hosts from further punishment. The Lions hammered 125 runs in 28 overs between lunch and tea as the bowlers served up numerous poor deliveries, and Cook and McKenzie were just getting into their stride when play was halted.