He combined in an excellent unbeaten partnership of 69 with nightwatchman Will Williams to take Lancashire to their target.
Lancashire had started the day needing 86 more runs to pull off a win to keep their Championship challenge alive with five wickets in hand.
Josh Bohannon fell early, shortly after reaching his century, a wicket that could have opened the door for the home side, but Washington and Williams (29 not out) kept their cool, increasing in confidence as they inched towards their target.
Northants, who had taken a late flurry of wickets the previous night, were buzzing when they took the field and buoyed further when Jack White, who skittled Lancashire in their first innings, removed Bohannon early.
It was to be their only breakthrough of the morning though as Washington and Williams continued to frustrate their efforts.
The result leaves Lancashire 31 points behind Surrey in the Division One table with four games to play.
Bohannon, 92 overnight, was expected to be the key man if Lancashire were to achieve victory.
His knock had helped keep Lancashire in the hunt as wickets fell on day three and he got the scoreboard moving by steering Ben Sanderson’s second legitimate delivery down to third for a boundary.
He moved to his century off 166 balls when he played Jack White aerially past a diving Emilio Gay at short midwicket, his 18th boundary of the innings.
His reprieve was short lived though as he fell to White’s next ball thanks to a stunning one handed grab at wide gully by skipper Will Young. It left Lancashire on 209 for six still needing 69 to win.
The usually dependable Sanderson, who claimed three wickets the previous evening, proved expensive initially, gifting Lancashire three no balls and leaking runs down the leg side, but challenged the batters as his radar started to fire, backed up well by White and Tom Taylor.
Young continued to rotate his bowlers against a watchful Washington and Williams who were content to take their time before unfurling some aggressive shots as they approached their target.
Washington confidently smashed a half volley from Simon Kerrigan through extra cover for four and late cut Rob Keogh for another boundary to take Lancashire past 250. When Northamptonshire took the new ball he confidently hit two leg-side boundaries against Sanderson.
Williams looked increasingly assured, running hard and bringing up the win with a late cut off Kerrigan for four.