After losing to Laois, a second straight defeat would have heaped early pressure on the new boss but a strong first-half performance - buttressed by the skills of Joe Sheridan - all but sealed victory by the interval.
The Yeats County kicked just three points in the opening half, only one coming from play. In contrast, the Leinster champions were full of running and their strong work ethic impressed McEnaney.
Sheridan brought the attack together, slamming in a 14th-minute shot that was parried to Brian Farrell for a tap-in goal. The score put Meath 1-3 to 0-1 clear and, from there, they strode to a comfortable victory. The only down side was a harsh red card, following two bookings, for wing-back Cormac McGuinness.
“(The win) means an awful lot,” McEnaney said. “We had a disappointing result in Portlaoise but the one thing I loved was the attitude when we got back training - it was first class. I knew for the last few days that we were going to put in a big performance.”
Sligo drew with Donegal in the first round and after the latter’s big win over Tyrone, good things were expected of Sligo. However, a Meath defence marshalled by full-back Kevin Reilly was rarely troubled. Captain Seamus Kenny was excellent, while Brian Meade seems a future option at centre-back.
Meath had amassed 1-7 to Sligo's 0-3 by half-time, with David Morgan faring well at corner-forward. Shane McAnarney, Graham Reilly and free-taker Shane O'Rourke were also on the score sheet.
When McAnarney and O'Rourke pointed again after the restart, the contest was virtually over at 1-9 to 0-4.
Sligo, at least, upped the ante. Driven on by roving All Star Charlie Harrison, they pushed Meath onto the back foot and dominated for 20 minutes or so in the half. Mark Breheny, sub Alan Costello and powerful midfielder Stephen Gilmartin all registered points.
But stylish Sheridan, now dropping deep to help out his defence, finished off a long, flowing move with a 66th minute point to kill off any hopes of a Sligo revival.
Scorers for Meath: S O'Rourke 0-4 (3f); B Farrell 1-0; J Sheridan, S McAnarney and G Reilly 0-2 each; D Morgan and T Walsh 0-1 each.
Sligo scorers: M Breheny (1f) and A Costello (0-2 each); A Marren, D Maye (1f), C Harrison, S Gilmartin (0-1) each.
MEATH: B Murphy; G O'Brien, K Reilly, C King; S Kenny, B Meade, C McGuinness; M Ward, C Gillespie; G Reilly, S O'Rourke, S McAnarney; D Morgan, J Sheridan, B Farrell.
Subs: D Dalton for Kenny (42), A Nestor for Farrell (61), N Crawford for M Ward (63), T Walsh for Morgan (65), C Ward for G Reilly (70), D Dalton for King (72).
SLIGO: P Greene; C Harrison, C Davey, R Donovan; K Cawley, M Quinn, P McGovern; T Taylor, S Gilmartin; M Breheny, E O'Hara, F Quinn; A Marren, D Kelly, D Maye.
Subs: B Kennedy for Davey (19), S Davey for Marren (half-time), B Egan for McGovern (43), A Costello for F Quinn (49), P Hughes for Maye (60).
Referee: R Hickey (Clare).