Josh Ruffels then struck two minutes later to claim his first senior goal and earn a point for third-placed Oxford.
"You have to be aware of the opposition sometimes and Bury are definitely in a false position," said Lewis. "They've had a big turn- over in players and I really think they're one of the best sides we've played.
"I think we counter-acted them well in the first half because they played three up front, with two out wide. They're a good side and we made it hard for them, but they made it hard for us at times because they keep passing it.
"Josh got in at the back post and fair play to him, he got up early to head in the equaliser. Then we made the substitutions and I thought Dave Kitson and David Connolly looked impressive. Connolly nearly got in a couple of times.
"In the last six league games we've won three and drawn three so that's good form, we just need to keep that going."
Bury striker Anton Forrester spurned an early chance with a tame header before Jean-Louis Akpa Akpro fired too close to visiting keeper Ryan Clarke.
Bury's positive start to the second half was rewarded when Chris Sedgwick's cross was spilled by Clarke and Jones fired into the open goal.
Oxford hit straight back as midfielder Ruffels, 20, headed home from Rose's corner.
Bury went closest to winning it as Clarke denied substitute Danny Nardiello and Andrew Tutte but a point was enough for them to climb three places to 17th.
The Shakers have now won three and lost just one of their last six games.
"Oxford have got the best away record in the league so they're resilient, that's why they're up there," said manager David Flitcroft.
"But we dragged them about, they've been tested, and they had to put a lot of miles in to try to keep us at bay.
"I'm frustrated with their goal but pleased with our progression. If you get there too fast it can be boom or bust. We've got a design over a length of time and we've still got 18 games left.
"We looked secure, we created some match-winning chances and we're getting better. We need to tidy up some details and if we can get it right in the final third then we're going to comfortably beat teams, especially here.