Batting first, the hosts amassed 194 for five thanks mainly to the big-hitting exploits of Cameron Delport (45 off 29 balls) and Cody Chetty (44 off 29).
The visitors were woeful in their reply and only managed 130 for nine with Maharaj bagging three for 23 and Subrayen claiming three for 21.
Tail-ender Corbin Bosch top scored with an unbeaten 30 as the Titans slumped to a third successive loss this season.
The Dolphins were off to a rollicking start thanks to Morne van Wyk and Delport, who took 21 from Ethy Mbhalati’s third over, as they raced to 50 in 24 balls.
Darren Sammy (2-29) struck the first blow with his fifth delivery when he had the captain caught behind by Mangaliso Mosehle for 37.
However, Chetty maintained the tempo alongside Delport as the pair added another 50 in only 32 balls – the 100 raised in the ninth over.
Sammy again broke the stand as he had Delport caught on the wide long-on fence.
Dean Elgar sent down an expensive two overs thereafter that came at a cost of 24, but he did claim the vital wicket of Chetty, excellently caught and bowled.
The hosts were still in prime position at 151 for three after 15 overs, but slightly lost their way towards the end after two wickets for Mbhalati (2-45) in the closing overs.
Vaughn van Jaarsveld’s 38 off 29 did, however, help the hosts at least set an above average 195.
The Titans made an equally good start to their chase with 23 coming in the first 2.4 overs.
But they then lost their way as Henry Davids (nine) and Roelof van der Merwe (10) fell chasing big shots with replacement fielder Divan van Wyk taking both catches off Craig Alexander and Robbie Frylinck respectively.
Morne van Wyk took the next catch, which was also a skier, as Dean Elgar (26) top-edged chasing a big shot to Subrayen.
The off-break bowler again struck in his next over to take out Cobus Pienaar (eight), caught by Delport at long off, and Theunis de Bruyn (14) gave fellow spinner Maharaj his first wicket when he was caught at long on by Divan.
At that stage, the Pretoria outfit were on 75 in 10.2 overs with half their team back in the changeroom.
Maharaj then dismissed Qaasim Adams (14) and Darren Sammy (one) from successive deliveries as things got even worse for the Titans, with Frylinck dismissing Tabraiz Shamzi (nought).