Haris made 89, while Babar scored 69 in Pakistan's strong performance with the bat.
Pakistan is taking on South Africa in Match 30 of World Cup at Lord's this Sunday (June 23).
Pakistan skipper Sarfaraz Ahmed won the toss and asked Faf du Plessis' South Africa to bowl first despite a tinge of greenery on the surface.
But the brave move paid off dividends as openers Imam-ul-Haq and Fakhar Zaman gave their team a fantastic start. Proteas' pacers overpitched the ball in trying to gain seam movement from the deck.
The opening duo stitched a very fine partnership of 81 runs before Fakhar (44) was dismissed off leg-spinner Imran Tahir, who soon got Imam (44) out too for an identical score.
Babar Azam and Mohammad Hafeez then stitched another stand of 45 runs. Hafeez scored 20 before part-timer Aiden Markram scalped him LBW. Babar continued, however, and got an able ally in Haris Sohail, who played some delightful strokes while the former rallied his way to a magnificent half-century. They kept increasing the run-rate as the innings approached the last 10 overs. South Africa didn't have much control over things.
The Proteas finally got a breakthrough again when Babar trying to up the ante was out caught on 69. Haris, though, completed his fifty soon at a brisk rate and tried to provide the innings a late flourish that Pakistan wanted. He went on to play one of the best innings of his career, scoring 89 off 59. Haris' stand-out knock was glint with nine fours and three sixes.
Imad Wasim (23), Wahab Riaz (4), Sarfaraz Ahmed (2*), Shadab Khan (1*) also tried big shots at the end as Pakistan finished with a strong total of 308/7 in 50 overs.
For South Africa, Kagiso Rabada (0/65), Lungi Ngidi (3/64), Chris Morris (0/61), Andile Phehlukwayo (1/49), Imran Tahir (2/41), Aiden Markram (1/22) failed to stop the run flow and left their team with a huge task in the second half.