The 36-year-old became the oldest man ever the honour and he is now looking to defend the title at the Indian Wells.
Federer was at his trademark best, fluid and graceful as the Swiss star broke in the fourth game for a 3-1 lead and never looked back. That came after a breakthrough 2017 which saw him win four titles, including Sofia, Cincinnati, Brisbane and the ATP Finals. The 36-year-old Spaniard is making his 16th consecutive appearance in Indian Wells, with his best result coming in 2015 (QF).
"It gave me a ton of inspiration for my upcoming matches", he said.
Verdasco's first serve proved almost unplayable in the deciding set of the second round match as he improved his career head-to-head record against Dimitrov to 2-2.
Once the third set began, it didn't take long for most observers to realize that it was Daniel's match to lose.
Djokovic's performance in the final set against the world's 109th-ranked player on centre court raised some eyebrows, with four-times grand slam champion Jim Courier saying the Serb had "capitulated".
Other seeded men advancing were: No. 7 Kevin Anderson defeated Evgeny Donskoy 7-5, 6-4, No. 12 Tomas Berdych rolled past German Maximilian Marterer 6-1, 6-4 in just over an hour.
"I was grateful to be out on the court after surgery that quickly but at the same time just didn't feel good at all. Just one of those days when you're not able to find the rhythm from the baseline, especially the backhand side".
"It felt like the first match I have ever played on the tour, very weird", he told reporters.
As for Djokovic, the question now is whether he will play in Miami later this month.
It was a determined Delbonis who looked to have been eased by the clearer conditions and he forced Federer to rescue a break point in the second game after the restart.
Federer's match was not the only one postponed by a persistent rain Saturday evening.
Daniel's third-round opponent is Argentina's Leonardo Mayer, who had been scheduled to play Japan's Kei Nishikori in the second round before the world No. 25 withdrew through illness. Earlier in the day, Feliciano Lopez dismissed wild card Ernesto Escobedo 6-4, 6-3 and awaits either eighth seed Jack Sock or Italy's Thomas Fabbiano.