A late try from George Pisi, converted by fly-half Stephen Myler, moved Northampton to the top of the Aviva Premiership table.
The final minutes saw the Saints camped out close to the Chiefs line searching for seven points to steal the victory and a series of five-metre scrums led to Samoan international Pisi breaching the line, with Myler converting.
The visitors looked dangerous in the opening minutes when they capitalised on a poor Chiefs line-out, before the game was halted when referee Greg Garner was unable to hear his two assistants or the TMO.
The break allowed the Chiefs to regroup but then their skipper Dean Mumm was sent to the sin- bin for stamping.
Even with a man down the Devon side won a penalty for a high tackle on Gareth Steenson and t he fly-half, with the wind at his back, slotted the ball between the uprights from 35 metres. However, he wa s just short of his target minutes later from outside on the left.
The Saints then applied the p ressure, ki cking a penalty to the corner before the forwards gained ground to allow lock Samu Manoa to offload for full-back James Wilson to cross for the first try of the game. Myler's conversion attempt hit the outside of the post.
Ten minutes before the break Northampton's Christian Day had to be helped from the pitch, before assistant referee Kelvin Stewart pulled a muscle.
Steenson pulled another long range penalty wide before finding his target to give the hosts the the lead.
TMO Ashley Rowden was then called into action to adjudicate on whether Samu Manoa had squeezed in at the corner or was bundled into touch. The former Premiership referee judged in the American international's favour to restore the Saints advantage.
Exeter kept battling away and another high tackle on Steenson in front of the posts allowed the half-back to land his third penalty to reduce the arrears at the break to 10-9 in a game were the conditions limited expansive play.
The Chiefs started the second half very lively and sought to take advantage of the extra man when Day's replacement Gj Van Velze was shown yellow for preventing the hosts taking a quick tap penalty.
They looked to have been rewarded for the efforts as centre Ian Whitten intercepted a pass to race 45 metres before being pulled down five metres from the line as he got the ball away to wing Matt Jess.
When the ball was worked wide flanker James Scaysbrook was judged by the TMO to have been held up over the line. From the scrum Lewis picked up and found a gap to cross the line with Steenson converting.
The conditions deteriorated as the game entered the final quarter but the Chiefs defence stood firm, with only a penalty to the corner breaching the opposition 22.
From the line-out the Saints crept closer to the line and referee Garner again called upon the TMO to deliberate. He ruled that the visitors were held up over the line, then the Chiefs were penalised at the resultant scrum.
With the Saints seeking a converted try to take the game they opted for another scrum and were again penalised. The third scrum stood up and the next attempt saw the ball pop out the back for the Chiefs to seize possession.
From a lineout Myler put a grubber kick through but replacement scrum-half Hayden Thomas collected and touched down.
However, yet another five-metre scrum saw Pisi burst through and Myler converted to break the Chiefs hearts.