Tenth seed Berdych next plays unseeded German Benjamin Becker
Tomas Berdych battled the elements and a gritty display by his unseeded Croatian opponent Ivan Dodig on Wednesday before sealing a 7-6(5) 5-7 6-1 7-6(2) win.
With the rain cutting a swathe through the programme for the second day running, the 10th-seeded Czech served for the match when play resumed after being called off with him leading 4-1 in the fourth set the previous day.
But in damp windy conditions that gradually turned to steady drizzle, and led to play being called off on all but one of Wimbledon's other outside courts, Dodig broke serve and saved two match points before taking the match to a tiebreak.
But Berdych, runner-up to Rafael Nadal at the All England Club in 2010 and contesting his 52nd consecutive grand slam, steadied his nerves to take the breaker 7-2 when he forced a backhand error from Dodig.
The Czech, vocal in his criticism of how French Open officials managed rain interruptions at Roland Garros earlier this month, next plays unseeded German Benjamin Becker.
Play on all outside courts was suspended until 1330 GMT, with further rain delays forecast into the evening.
Centre Court action began on time with the roof closed.
Defending champion Novak Djokovic will take on Frenchman Adrian Mannarino before seven-times champion Roger Federer plays Britain's world number 772 Marcus Willis.