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The 28-year-old Kenyan-born rider took over from Friday's fourth-stage winner, Slovakia's Peter Sagan, at the head of the overall standings.
Froome came home ahead of American Tejay van Garderen and Colombian Rigoberto Uran on the stage which finished at Jabal Al Akhdar, on the side of the Green Mountain.
The Team Sky leader is 26 seconds clear of Van Garderen ahead of Sunday's final stage, which finishes on the Corniche at Muscat.
"I am really very, very happy because it was an extremely difficult climb and to win this stage means you always also take a huge psychological advance on the others," said Froome.
"The goal today (Saturday) was to see where I was in terms of race fitness.
"I got positive answers to my questions. It is an agreeable feeling to be ahead of schedule so early in the season.
Froome, though, said that it was too early to draw any conclusions as to the defence of his Tour title.
"To win here has merely psychological value more than anything else," he said.
"The Tour is still a long way away. But morale-wise with regard to the competition, it is true that does me good."
Results of the Tour of Oman fifth and penultimate stage, a 147.5km ride from Muscat to Jabal Al Akhdar (Green Mountain) on Saturday:
1. Christopher Froome (GBR/Sky), 3hr 49min 53sec, 2. Tejay Van Garderen (USA) at 22s, 3. Rigoberto Uran (COL) at 33s, 4. Joaquim Rodriguez (ESP) at 38s, 5. Robert Gesink (NED) at 47s, 6. Domenico Pozzovivo (ITA) at 51s, 7. Arnold Jeannesson (FRA) at 56s, 8. Romain Bardet (FRA) at 59s, 9. Sergio Henao (COL) at 1min 09s, 10. Roman Kreuziger (CZE) at 1min 15s.
Overall standings
1. Christopher Froome (GBR/Sky), 18hr 36min 45sec, 2. Tejay Van Garderen (USA) at 26s, 3. Rigoberto Uran (COL) at 31s, 4. Joaquim Rodriguez (ESP) at 48s, 5. Robert Gesink (NED) at 57s, 6. Domenico Pozzovivo (ITA) at 1min 01s, 7. Sergio Henao (COL) at 1min 19s, 8. Roman Kreuziger (CZE) at 1min 55s, 9. Johann Tschopp (SUI) at 1min 32s, 10. Daniel Moreno (ESP) at 1min 34s.
