"A lot hinged on that first restart, passing Will there," Franchitti said. "I forced the issue fairly aggressively, I think. I was going for it."
Franchitti, 37, took Chip Ganassi Racing to victory lane in St. Petersburg for the first time.
"Chip was fairly happy," Franchitti said.
Pole sitter and defending race champion Power finished second, 7.1612 seconds behind, in the season opener.
"Dario beat me again," Power said, managing a smile. "Dario got me fair and square with a move around the outside." Power added that he fell to seventh when his engine went into neutral after his car was hit on an early restart.
Tony Kanaan was third in his debut for KV Racing, which signed him last Monday. He was pleased, especially on the heels of an offseason in which he lost two rides because of sponsorship issues.
"I think [with] chemistry, you either click right away or you don't," Kanaan said. "I always approve of having a good atmosphere on the team. I think we do."
Two drivers recorded career bests to round out the top five: HVM's Simona de Silvestro and KV Racing's Takuma Sato.
The race had a rough start, with four caution flags in the first 14 laps. An accident in the first turn of Lap 1 ended the hopes of five contenders.
Marco Andretti flipped his car after hitting Scott Dixon's car under braking for the right-hand turn. Andretti landed upside down but walked back to pit lane, apparently unhurt.
Andretti, who said two-time St. Petersburg winner Helio Castroneves hit him from behind entering the turn, was eliminated along with Andretti Autosport teammate Mike Conway. Dixon, Castroneves and 2009 St. Petersburg winner Ryan Briscoe reentered the race several laps down after their teams made repairs.
"It was a start, NASCAR style," said Power, whose car wasn't touched as the mayhem broke out behind him. "And we are not NASCAR. … We can't hit each other."
Franchitti's big move came on the ensuing restart, and once he took over, he was unstoppable, losing the top spot to Power for just two laps after a pit stop on Lap 71. Once Power made his pit stop, Franchitti kept a six- to seven-second gap until the end.
The Scotsman also got an early edge on the nonoval portion of the season, during which Power won five times last year, including three times on street circuits.
"We have won the odd street race ourselves," said Franchitti, who tied Johnny Rutherford for 10th on the career list of North American open-wheel series victories with his 27th. "It's the best road-course car I think I've had since I came to the team [in 2009]. Things could change in a minute though.
"Barber could be interesting," Franchitti continued, referring to Barber Motorsports Park in Birmingham, Ala., site of the next series race April 10. "But if there's a team I want to be with in those situations, it's the Target [Ganassi] team."
AT ST. PETERSBURG (FLA.) STREET CIRCUIT
Lap length: 1.8 miles
(Start position in parentheses)
All cars Dallara chassis, Honda engine
1. (2) Dario Franchitti, 100 laps.
2. (1) Will Power, 100.
3. (8) Tony Kanaan, 100.
4. (17) Simona de Silvestro, 100.
5. (11) Takuma Sato, 100.
6. (10) Alex Tagliani, 100.
7. (16) Raphael Matos, 100.
8. (13) Vitor Meira, 100.
9. (15) Oriol Servia, 100.
10. (6) Justin Wilson, 100.
11. (25) J.R. Hildebrand, 100.
12. (19) Danica Patrick, 100.
13. (24) Sebastian Saavedra, 98.
14. (20) Ana Beatriz, 98.
15. (22) James Jakes, 97.
16. (3) Scott Dixon, 96.
17. (12) Graham Rahal, 96.
18. (5) Ryan Briscoe, 95.
19. (21) E.J. Viso, 94.
20. (9) Helio Castroneves, 85.
21. (14) Ryan Hunter-Reay, 58, handling.
22. (23) Charlie Kimball, 38, contact.
23. (4) Mike Conway, 1, contact.
24. (7) Marco Andretti, 0, contact.
25. (18) Sebastien Bourdais, 0, did not start.
Winner's average speed: 89.260 mph. Time of race: 2 hours, 0 minutes, 59.6886 of a second. Margin of victory: 7.1612 seconds.
Cautions: 5 for 13 laps. Lead changes: 3 among 2 drivers. Lap leaders: Power 1-4, Franchitti 5-70, Power 71-72, Franchitti 73-100.
Points: Franchitti 52, Power 41, Kanaan 35, de Silvestro 32, Sato 30, Tagliani 28, Matos 26, Meira 24, Servia 22, Wilson 20.
If you go
BALTIMORE GRAND PRIX FESTIVAL OF SPEED
What: Auto racing festival, featuring IndyCar Series open-wheel race
When: Sept. 2-4
Where: Downtown Baltimore
Tickets: Available at baltimoregrandprix.com or by calling Ticketfly at 877-435-9849.
Rows 1-10: Adult, $130; ages 12 and under, $100
Rows 11+: Adult, $160; ages 12 and under, $125
Rows 1-10: Adult, $75; ages 12 and under, $60
Rows 11+: Sold out
Rows 1-10: Adult, $65; ages 12 and under, $50
Rows 11+: Adult, $75; ages 12 and under, $60
Three-day: Adult, $65; ages 12 and under, $50
Sunday: Adult, $45; ages 12 and under, $30
Saturday: Adult, $30; ages 12 and under, $20
Friday: Adult, $20; ages 12 and under, $15