Overseas man Rizwan Ahmed made his debut at Saltaire and returned impressive figures of 3-31 in 15 overs.
Imran Patel (3-44) and Chris Schofield (4-9) also shone with the ball as Saltaire were bowled out for 138, having made an encouraging start at 43-0.
Former Heaton man Javed Umarji (33) was Saltaire's top scorer, while fellow opener Wasim Munawar (29) also chipped in.
Heaton were wobbling at 29-3 in reply before Schofield and James Stansfield (34) steadied the ship.
Opener Schofield ended 34 not out as Heaton edged home with seven balls to spare, earning 16 points, which leaves them sixth in the table.
On Sunday, Heaton slipped to a 93-run defeat against Yeadon, who have lost their opening three league games.
Yeadon overseas batsman Aamir Sajjad smashed 115 in his side's 248-8.
Haroon Rashid (52) and brother Amar (41) shone but the visitors collapsed to 155 all out against the spin of Andrew Robertson (5-24).
Heaton's Second team are third in Division One after a comprehensive 196-run victory over Cleckheaton last Saturday.
Opening batsman Robert Smith carried his bat for 123, in an innings that included 10 fours and four sixes.
Support came from Dave Lawrence (54), Howard Ellis (42) and Chris Goodair (30no) as Heaton posted 283-4.
Ben Gilbert claimed 5-25 in reply and with Adeel Hafeez (3-8) supporting, Cleckheaton were all out for 87.
n Heaton Seconds have been drawn away to Idle in the second round of the Priestley Shield on June 1.