The victory enabled the AL East leaders to maintain their 4½-game advantage over the Orioles, who were seeking to deal the Blue Jays their third straight series loss.
"It means a lot," Navarro said.
"It's a good series in general. We made some good plays, we got some clutch hitting," Toronto slugger Jose Bautista said. "A series split on the road against the second-place team is something to not be too upset about."
Edwin Encarnacion also had three hits for the Blue Jays, who had totaled 15 runs in losing six of their previous eight games. Led by Navarro, Toronto banged out 12 hits against Chris Tillman and two relievers.
Navarro had two doubles and a single.
"I know people expect the runs to come from the big boys," he said. "You cannot always depend on the big dogs. You can count on the little guys sometimes."
Happ (6-3) gave up one run, seven hits and no walks in six-plus innings. He had lost two of his previous three starts, yielding 12 earned runs over 17 2/3 innings.
"Happ was outstanding, he really was," manager John Gibbons said. "He gave us a chance to win out there."
Casey Janssen got four outs for his 12th save.
"We've played some really good teams," Jones said. "The competitive level is rising and it's fun to see."
Tillman (5-4) allowed three runs and eight hits in seven innings. The right-hander didn't issue a walk or record a strikeout, only the sixth time in Orioles history that's happened for a pitcher who went at least seven innings.
"It was a good series," Tillman said. "We would have liked to have to come out on top, but we split against the team that's leading the league. Just come back better next time."
Tillman is 0-4 with a 2.78 ERA at home and 5-0 with a 6.33 ERA on the road.
"That's how it goes in baseball," Jones said. "He threw the ball well today. Unfortunately, we were unable to score him some runs. We had a couple opportunities, but he can only do what he can control."
"A couple of runs late can be wonderful," Gibbons said.
Jones hit his 11th homer of the season in the bottom half off Dustin McGowan, but Janssen made sure the Orioles wouldn't score again.
"The goal is always to win series," Happ said, "but to split is pretty good, too."
Toronto got a first-inning run on an RBI double by Bautista, who one pitch earlier thought he had drawn a walk on a 3-1 offering that umpire Jerry Layne called a strike.
The Blue Jays wasted a leadoff double in the second inning but converted the same situation in the fourth. After Encarnacion doubled, Navarro blooped an RBI single to left field for a 2-0 lead.
Baltimore closed to 3-1 in the sixth when Jones hit a two-out double and Cruz singled him home.
It was the first time since May 27, 2010, against Oakland that Baltimore pitchers did not record a single strikeout. ... Orioles 1B Chris Davis was given a rare day off by manager Buck Showalter, even though the slugger had four homers in his last 11 games. ... Two Toronto pitchers who left with groin tightness this weekend remained hopeful of avoiding the disabled list. After receiving treatment, Brett Cecil said, "I'm sure I'll feel it when I throw," and R.A. Dickey said of his injury: "Maybe a little sore, but not bad." ... The Blue Jays have Monday off, while the Orioles continue a 13-game run against AL East foes in Tampa Bay against the last-place Rays. ... Umpire Hunter Wendelstedt was scratched, one day after he fell backward and hit his head upon being unintentionally brushed by Jones. ... The crowd of 46,469 was Baltimore's fifth sellout of the season and second in the series.