Beavers have long battled humans over the flow of water, and they usually end up on the losing side. But a pair of the aquatic rodents plying a patch of wetlands in Lawrence were so crafty that they apparently outwitted state officials, at least briefly.

In the past few weeks, a dam built by the long-residing duo in the wetlands adjacent to Den Rock Park sent water flooding onto nearby Route 114.

Officials from the Massachusetts Highway Department moved in with backhoes and breached the dam to drain the flooded road, which was experiencing dangerous driving conditions.

But as often happens in such struggles with beavers, the numbers of which have increased dramatically in the past decade in Massachusetts, the animals quickly rebuilt their dam.

The smart-thinking officials decided to fight back by sticking a long, plastic pipe through the dam, which accomplished the same goal as before, again draining the road and lowering the water level in the surrounding pond.

But the indefatigable beavers weren’t fooled. They ripped off some tree branches and used mud to clog the pipe’s small opening.

"It’s certainly not uncommon to have to breach a beaver dam multiple times," said Adam Hurtubise, a spokesman for the Highway Department.

But this time, they had to build a cage around the pipe to keep the beavers at bay and allow the water to flow through the culvert beneath Route 114 and into the Shawsheen River.

The frustration experienced by state officials isn’t uncommon where nature meets development, and the aggravation is often intense for local officials such as Tennis Lilly, chairman of the Lawrence Conservation Commission.

He often finds himself trying to placate angry homeowners who may have had their basement or driveway flooded. He also has to ensure nature takes its course.

"I have never taken as much grief over anything as I have with beavers, Lilly said. "They are very unpopular animals."

Beavers have multiplied since the state banned leg-hold traps in 1997. There are now an estimated 60,000 to 90,000 beavers in Massachusetts, up from about 10,000 a decade ago, Lilly said.

The rise in their population has created more conflicts as they encroach on development. But Lilly has a responsibility to preserve the ecosystem and notes that the dams beavers build help attract more wildlife to the area.

He said Den Rock Park is now home to more swallows, herons, wood ducks, mallards, spotted salamanders, wood turtles, frogs, river otters, and mink, among other wildlife, than it had been in years.

"Beavers have an impact well beyond their presence, he said. "The key is we need to learn to coexist."