The Titans, who won the toss and chose to bat, had 167 for two, with Rudolph poised on 93.
The Titans got off to a steady start, scoring 100 for the loss of two wickets in the first session.
Blake Snijman was first to go, caught behind by Heino Kuhn off Vernon Philander for 18. Gulam Bodi was in the middle for just under half-an-hour before he was trapped leg before wicket for five.
Farhaan Behardien joined his captain and wasted no time in getting among the runs. Their 50 run partnership came off 84 balls, and the 100 off 157.
Rudolph's half century - the 63rd of his career came at a run a ball, and took him just over two hours.
Rudolph, who has ended his contract with English county Yorkshire, was in sublime form as he stroked 14 fours and a six on his way to 93.
He could well be in contention for a return to the national team after an absence of four years.
His last Test appearance was against Sri Lanka in Colombo in 2006, but he could force the selectors to give him another chance by sheer weight of runs in domestic cricket.
In the first match of the season last week, he made an excellent 72 in the Titans' first innings as they defeated the Warriors by nine wickets.
Behardien was not out on 46 at close of play, four short of his 16th first class half century.
Vernon Philander was the most economical of the Cobras' bowlers, with one wicket for 29 runs off his 12 overs.
Charl Langeveldt conceded 46 off his 14, Monde Zondeki 30 off 10 overs, and Henderson was the most expensive, going for 61 runs for one wicket off 14 overs.